%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU429+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 : n011.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 08:38:51 AM UTC 2026
% Result : Theorem 109.28s 54.86s
% Output : Refutation 115.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2594
% Syntax : Number of formulae : 5190 ( 697 unt; 0 typ; 0 def)
% Number of atoms : 27485 (5499 equ; 0 cnn)
% Maximal formula atoms : 47 ( 5 avg)
% Number of connectives : 105695 (4282 ~; 276 |;10868 &;79118 @)
% ( 445 <=>;10706 =>; 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 : 588 ( 586 usr; 127 con; 0-10 aty)
% Number of variables : 17855 ( 0 ^;16937 !; 918 ?;17855 :)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(a_4_1_relset_2_decl,type,
a_4_1_relset_2: $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_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
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(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k7_relat_1_decl,type,
k7_relat_1: $i > $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k10_finseq_1_decl,type,
k10_finseq_1: $i > $i > $i ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_mcart_1_decl,type,
k1_mcart_1: $i > $i ).
thf(k2_mcart_1_decl,type,
k2_mcart_1: $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k2_funct_4_decl,type,
k2_funct_4: $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(k9_setwiseo_decl,type,
k9_setwiseo: $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k13_funct_3_decl,type,
k13_funct_3: $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k1_cat_1_decl,type,
k1_cat_1: $i > $i > $i > $i ).
thf(k1_numbers_decl,type,
k1_numbers: $i ).
thf(k9_binop_2_decl,type,
k9_binop_2: $i > $i > $i ).
thf(k4_funcop_1_decl,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(k3_funcop_1_decl,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(k2_funcop_1_decl,type,
k2_funcop_1: $i > $i > $i ).
thf(m2_pua2mss1_decl,type,
m2_pua2mss1: $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(m2_finseq_2_decl,type,
m2_finseq_2: $i > $i > $i > $o ).
thf(k4_finseq_2_decl,type,
k4_finseq_2: $i > $i > $i ).
thf(k4_finseq_1_decl,type,
k4_finseq_1: $i > $i ).
thf(k2_finseq_1_decl,type,
k2_finseq_1: $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(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(k19_mcart_1_decl,type,
k19_mcart_1: $i > $i ).
thf(k4_funct_4_decl,type,
k4_funct_4: $i > $i > $i > $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(r6_binop_1_decl,type,
r6_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(k1_setwiseo_decl,type,
k1_setwiseo: $i > $i ).
thf(r1_binop_1_decl,type,
r1_binop_1: $i > $i > $i > $o ).
thf(m3_pboole_decl,type,
m3_pboole: $i > $i > $i > $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(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
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(k4_card_3_decl,type,
k4_card_3: $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(m2_finseq_1_decl,type,
m2_finseq_1: $i > $i > $o ).
thf(k12_finseq_1_decl,type,
k12_finseq_1: $i > $i > $i ).
thf(k11_binop_2_decl,type,
k11_binop_2: $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k10_binop_2_decl,type,
k10_binop_2: $i > $i > $i ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k7_pboole_decl,type,
k7_pboole: $i > $i > $i > $i > $i ).
thf(k11_finseq_1_decl,type,
k11_finseq_1: $i > $i > $i > $i ).
thf(k3_funct_4_decl,type,
k3_funct_4: $i > $i > $i ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(k4_setwiseo_decl,type,
k4_setwiseo: $i > $i > $i > $i > $i ).
thf(k18_mcart_1_decl,type,
k18_mcart_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(k9_finseq_1_decl,type,
k9_finseq_1: $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(k3_cqc_lang_decl,type,
k3_cqc_lang: $i > $i > $i ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(k9_funct_2_decl,type,
k9_funct_2: $i > $i > $i > $i ).
thf(k1_funct_5_decl,type,
k1_funct_5: $i > $i ).
thf(k2_funct_5_decl,type,
k2_funct_5: $i > $i ).
thf(k2_ens_1_decl,type,
k2_ens_1: $i > $i ).
thf(k3_ens_1_decl,type,
k3_ens_1: $i > $i > $i ).
thf(k4_ens_1_decl,type,
k4_ens_1: $i > $i > $i ).
thf(k6_ens_1_decl,type,
k6_ens_1: $i > $i > $i > $i ).
thf(v1_finseq_1_decl,type,
v1_finseq_1: $i > $o ).
thf(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(r6_pboole_decl,type,
r6_pboole: $i > $i > $i > $o ).
thf(k2_midsp_1_decl,type,
k2_midsp_1: $i ).
thf(k7_vectsp_2_decl,type,
k7_vectsp_2: $i ).
thf(k8_vectsp_2_decl,type,
k8_vectsp_2: $i ).
thf(k5_funcop_1_decl,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(k4_relset_2_decl,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k3_urysohn1_decl,type,
k3_urysohn1: $i > $i ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(k10_ens_1_decl,type,
k10_ens_1: $i > $i ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k8_setwiseo_decl,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k15_funct_3_decl,type,
k15_funct_3: $i > $i > $i ).
thf(k33_binop_2_decl,type,
k33_binop_2: $i ).
thf(k6_funcop_1_decl,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k8_funcop_1_decl,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k12_mcart_1_decl,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(k7_filter_1_decl,type,
k7_filter_1: $i > $i > $i > $i > $i ).
thf(v1_classes2_decl,type,
v1_classes2: $i > $o ).
thf(k9_funct_3_decl,type,
k9_funct_3: $i > $i > $i ).
thf(k35_binop_2_decl,type,
k35_binop_2: $i ).
thf(m2_filter_1_decl,type,
m2_filter_1: $i > $i > $i > $o ).
thf(k1_funct_3_decl,type,
k1_funct_3: $i > $i ).
thf(k4_relset_1_decl,type,
k4_relset_1: $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(k17_mcart_1_decl,type,
k17_mcart_1: $i > $i ).
thf(k3_setwiseo_decl,type,
k3_setwiseo: $i > $i > $i > $i ).
thf(k4_partfun1_decl,type,
k4_partfun1: $i > $i > $i ).
thf(k1_enumset1_decl,type,
k1_enumset1: $i > $i > $i > $i ).
thf(k1_metric_1_decl,type,
k1_metric_1: $i > $i > $i > $i > $i > $i ).
thf(k12_binop_2_decl,type,
k12_binop_2: $i > $i > $i ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(k12_funct_3_decl,type,
k12_funct_3: $i > $i ).
thf(k10_setwiseo_decl,type,
k10_setwiseo: $i > $i > $i > $i > $i ).
thf(k16_funct_3_decl,type,
k16_funct_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(k6_enumset1_decl,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_decl,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(m1_card_fil_decl,type,
m1_card_fil: $i > $i > $o ).
thf(v2_card_fil_decl,type,
v2_card_fil: $i > $i > $o ).
thf(v3_card_fil_decl,type,
v3_card_fil: $i > $i > $o ).
thf(k5_enumset1_decl,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k3_enumset1_decl,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(k4_zfmisc_1_decl,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(k4_mcart_1_decl,type,
k4_mcart_1: $i > $i > $i > $i > $i ).
thf(v1_realset1_decl,type,
v1_realset1: $i > $o ).
thf(m4_realset1_decl,type,
m4_realset1: $i > $i > $o ).
thf(k8_mcart_1_decl,type,
k8_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k3_zfmisc_1_decl,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(k3_mcart_1_decl,type,
k3_mcart_1: $i > $i > $i > $i ).
thf(k5_xboole_0_decl,type,
k5_xboole_0: $i > $i > $i ).
thf(k5_relset_1_decl,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k1_setfam_1_decl,type,
k1_setfam_1: $i > $i ).
thf(v6_ordinal1_decl,type,
v6_ordinal1: $i > $o ).
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(k1_relset_2_decl,type,
k1_relset_2: $i > $i > $i > $i ).
thf(k3_setfam_1_decl,type,
k3_setfam_1: $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v4_finsub_1_decl,type,
v4_finsub_1: $i > $o ).
thf(k1_finsub_1_decl,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k9_mcart_1_decl,type,
k9_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k8_binop_2_decl,type,
k8_binop_2: $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k5_mcart_1_decl,type,
k5_mcart_1: $i > $i > $i > $i > $i ).
thf(k6_mcart_1_decl,type,
k6_mcart_1: $i > $i > $i > $i > $i ).
thf(k7_mcart_1_decl,type,
k7_mcart_1: $i > $i > $i > $i > $i ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k6_pralg_1_decl,type,
k6_pralg_1: $i > $i > $i ).
thf(k10_mcart_1_decl,type,
k10_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k11_mcart_1_decl,type,
k11_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k12_ens_1_decl,type,
k12_ens_1: $i > $i ).
thf(g1_cat_1_decl,type,
g1_cat_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k8_ens_1_decl,type,
k8_ens_1: $i > $i ).
thf(k9_ens_1_decl,type,
k9_ens_1: $i > $i ).
thf(k11_ens_1_decl,type,
k11_ens_1: $i > $i ).
thf(k4_qc_lang1_decl,type,
k4_qc_lang1: $i ).
thf(k2_qc_lang1_decl,type,
k2_qc_lang1: $i ).
thf(k6_cqc_lang_decl,type,
k6_cqc_lang: $i > $i > $i ).
thf(k18_group_2_decl,type,
k18_group_2: $i > $i > $i ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(k4_realset1_decl,type,
k4_realset1: $i > $i > $i > $i ).
thf(k2_borsuk_1_decl,type,
k2_borsuk_1: $i > $i > $i ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k7_cat_1_decl,type,
k7_cat_1: $i > $i > $i ).
thf(a_0_0_altcat_2_decl,type,
a_0_0_altcat_2: $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(k10_relset_1_decl,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(k11_relset_1_decl,type,
k11_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(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k4_funct_2_decl,type,
k4_funct_2: $i > $i > $i > $i ).
thf(v1_fraenkel_decl,type,
v1_fraenkel: $i > $o ).
thf(k2_cantor_1_decl,type,
k2_cantor_1: $i > $i > $i ).
thf(a_3_1_pua2mss1_decl,type,
a_3_1_pua2mss1: $i > $i > $i > $i ).
thf(k2_enumset1_decl,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(k36_binop_2_decl,type,
k36_binop_2: $i ).
thf(k10_pboole_decl,type,
k10_pboole: $i > $i > $i ).
thf(k13_pboole_decl,type,
k13_pboole: $i > $i > $i ).
thf(k7_ens_1_decl,type,
k7_ens_1: $i > $i > $i > $i ).
thf(r4_nattra_1_decl,type,
r4_nattra_1: $i > $i > $i > $i > $i > $i > $o ).
thf(k2_card_fil_decl,type,
k2_card_fil: $i > $i > $i ).
thf(m1_fraenkel_decl,type,
m1_fraenkel: $i > $i > $i > $o ).
thf(k1_cat_2_decl,type,
k1_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(m1_filter_1_decl,type,
m1_filter_1: $i > $i > $i > $o ).
thf(k7_metric_1_decl,type,
k7_metric_1: $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(k9_cat_2_decl,type,
k9_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k9_funcop_1_decl,type,
k9_funcop_1: $i > $i > $i > $i > $i ).
thf(k11_setwiseo_decl,type,
k11_setwiseo: $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(k14_funct_3_decl,type,
k14_funct_3: $i > $i > $i > $i > $i > $i ).
thf(r2_realset1_decl,type,
r2_realset1: $i > $i > $i > $o ).
thf(k7_binop_2_decl,type,
k7_binop_2: $i > $i ).
thf(k4_domain_1_decl,type,
k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k5_ens_1_decl,type,
k5_ens_1: $i > $i > $i ).
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(r2_subset_1_decl,type,
r2_subset_1: $i > $i > $o ).
thf(k2_monoid_0_decl,type,
k2_monoid_0: $i > $i > $i > $i ).
thf(k3_cantor_1_decl,type,
k3_cantor_1: $i > $i > $i > $i > $i > $i ).
thf(k1_pcomps_1_decl,type,
k1_pcomps_1: $i > $i ).
thf(k14_borsuk_1_decl,type,
k14_borsuk_1: $i > $i > $i > $i > $i ).
thf(k1_card_fil_decl,type,
k1_card_fil: $i > $i > $i ).
thf(k6_setfam_1_decl,type,
k6_setfam_1: $i > $i > $i ).
thf(a_1_0_ens_1_decl,type,
a_1_0_ens_1: $i > $i ).
thf(m1_finseq_2_decl,type,
m1_finseq_2: $i > $i > $o ).
thf(k7_subset_1_decl,type,
k7_subset_1: $i > $i > $i > $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(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(k1_toler_1_decl,type,
k1_toler_1: $i > $i > $i ).
thf(u1_cat_1_decl,type,
u1_cat_1: $i > $i ).
thf(k2_functor0_decl,type,
k2_functor0: $i > $i > $i > $i > $i > $i > $i ).
thf(a_6_0_functor0_decl,type,
a_6_0_functor0: $i > $i > $i > $i > $i > $i > $i ).
thf(a_4_0_domain_1_decl,type,
a_4_0_domain_1: $i > $i > $i > $i > $i ).
thf(k6_relset_2_decl,type,
k6_relset_2: $i > $i > $i > $i ).
thf(k15_classes2_decl,type,
k15_classes2: $i > $i ).
thf(k10_funcop_1_decl,type,
k10_funcop_1: $i > $i > $i > $i > $i ).
thf(r1_lattice2_decl,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(a_3_0_domain_1_decl,type,
a_3_0_domain_1: $i > $i > $i > $i ).
thf(k1_nattra_1_decl,type,
k1_nattra_1: $i > $i > $i > $i > $i ).
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(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k34_binop_2_decl,type,
k34_binop_2: $i ).
thf(v1_yellow18_decl,type,
v1_yellow18: $i > $i > $i > $i > $o ).
thf(m1_orders_1_decl,type,
m1_orders_1: $i > $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(k2_funct_3_decl,type,
k2_funct_3: $i > $i > $i > $i ).
thf(k1_cantor_1_decl,type,
k1_cantor_1: $i > $i > $i ).
thf(k1_funct_7_decl,type,
k1_funct_7: $i > $i > $i ).
thf(k1_qc_lang1_decl,type,
k1_qc_lang1: $i ).
thf(g1_group_1_decl,type,
g1_group_1: $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(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(k1_orders_1_decl,type,
k1_orders_1: $i > $i ).
thf(k3_relset_2_decl,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k1_ens_1_decl,type,
k1_ens_1: $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(k13_ens_1_decl,type,
k13_ens_1: $i > $i > $i ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(k7_setfam_1_decl,type,
k7_setfam_1: $i > $i > $i ).
thf(k5_funcsdom_decl,type,
k5_funcsdom: $i > $i > $i > $i > $i > $i ).
thf(k9_zf_lang_decl,type,
k9_zf_lang: $i ).
thf(r1_zfrefle1_decl,type,
r1_zfrefle1: $i > $i > $o ).
thf(r3_zfrefle1_decl,type,
r3_zfrefle1: $i > $i > $o ).
thf(r2_zfrefle1_decl,type,
r2_zfrefle1: $i > $i > $o ).
thf(v2_cat_5_decl,type,
v2_cat_5: $i > $o ).
thf(m1_cat_5_decl,type,
m1_cat_5: $i > $i > $o ).
thf(k3_classes2_decl,type,
k3_classes2: $i > $i > $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(k8_classes2_decl,type,
k8_classes2: $i > $i > $i > $i ).
thf(v2_setfam_1_decl,type,
v2_setfam_1: $i > $o ).
thf(k9_relset_1_decl,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(v1_zf_model_decl,type,
v1_zf_model: $i > $o ).
thf(k2_zfrefle1_decl,type,
k2_zfrefle1: $i ).
thf(k1_borsuk_1_decl,type,
k1_borsuk_1: $i > $i > $i > $i ).
thf(k15_ens_1_decl,type,
k15_ens_1: $i > $i > $i ).
thf(u2_cat_1_decl,type,
u2_cat_1: $i > $i ).
thf(k9_classes2_decl,type,
k9_classes2: $i > $i > $i > $i ).
thf(k4_classes2_decl,type,
k4_classes2: $i > $i > $i ).
thf(g1_lattices_decl,type,
g1_lattices: $i > $i > $i ).
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(m2_card_fil_decl,type,
m2_card_fil: $i > $i > $o ).
thf(k8_waybel_5_decl,type,
k8_waybel_5: $i > $i > $i > $i > $i ).
thf(v5_grcat_1_decl,type,
v5_grcat_1: $i > $o ).
thf(m3_grcat_1_decl,type,
m3_grcat_1: $i > $i > $o ).
thf(k2_subset_1_decl,type,
k2_subset_1: $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(a_1_2_ens_1_decl,type,
a_1_2_ens_1: $i > $i ).
thf(a_2_0_lattice5_decl,type,
a_2_0_lattice5: $i > $i > $i ).
thf(k8_relset_2_decl,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k11_classes2_decl,type,
k11_classes2: $i > $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(g3_quantal1_decl,type,
g3_quantal1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s2_multop_1_decl,type,
f1_s2_multop_1: $i ).
thf(p1_s2_multop_1_decl,type,
p1_s2_multop_1: $i > $i > $i > $i > $o ).
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(k3_qc_lang1_decl,type,
k3_qc_lang1: $i ).
thf(k5_urysohn1_decl,type,
k5_urysohn1: $i ).
thf(k9_relset_2_decl,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(k10_classes2_decl,type,
k10_classes2: $i > $i > $i > $i ).
thf(v1_tex_2_decl,type,
v1_tex_2: $i > $i > $o ).
thf(k3_card_fil_decl,type,
k3_card_fil: $i > $i > $i > $i ).
thf(v4_orders_3_decl,type,
v4_orders_3: $i > $o ).
thf(k2_yellow21_decl,type,
k2_yellow21: $i > $i ).
thf(k6_classes2_decl,type,
k6_classes2: $i > $i > $i > $i ).
thf(k4_finsub_1_decl,type,
k4_finsub_1: $i > $i > $i > $i ).
thf(k3_funcsdom_decl,type,
k3_funcsdom: $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(k2_relset_2_decl,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(a_3_0_ens_1_decl,type,
a_3_0_ens_1: $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(k12_classes2_decl,type,
k12_classes2: $i > $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(m1_orders_3_decl,type,
m1_orders_3: $i > $i > $o ).
thf(k19_pralg_1_decl,type,
k19_pralg_1: $i > $i > $i > $i ).
thf(a_2_0_borsuk_1_decl,type,
a_2_0_borsuk_1: $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(k2_yellow_3_decl,type,
k2_yellow_3: $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_1_yellow_9_decl,type,
a_4_1_yellow_9: $i > $i > $i > $i > $i ).
thf(a_4_0_pua2mss1_decl,type,
a_4_0_pua2mss1: $i > $i > $i > $i > $i ).
thf(k1_cqc_lang_decl,type,
k1_cqc_lang: $i > $i > $i > $i > $i ).
thf(k1_cat_5_decl,type,
k1_cat_5: $i > $i > $i > $i > $i ).
thf(f1_s4_funct_2_decl,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_decl,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_decl,type,
f3_s4_funct_2: $i > $i ).
thf(k1_urysohn1_decl,type,
k1_urysohn1: $i ).
thf(k2_urysohn1_decl,type,
k2_urysohn1: $i ).
thf(k7_relset_2_decl,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(k17_domain_1_decl,type,
k17_domain_1: $i > $i > $i > $i > $i ).
thf(k7_classes2_decl,type,
k7_classes2: $i > $i > $i > $i ).
thf(a_3_1_card_fil_decl,type,
a_3_1_card_fil: $i > $i > $i > $i ).
thf(k6_lattice5_decl,type,
k6_lattice5: $i > $i ).
thf(g1_funcsdom_decl,type,
g1_funcsdom: $i > $i > $i > $i > $i > $i > $i ).
thf(k15_domain_1_decl,type,
k15_domain_1: $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(a_1_0_pua2mss1_decl,type,
a_1_0_pua2mss1: $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(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(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(k14_domain_1_decl,type,
k14_domain_1: $i > $i > $i > $i > $i ).
thf(k4_card_fil_decl,type,
k4_card_fil: $i > $i ).
thf(m1_cantor_1_decl,type,
m1_cantor_1: $i > $i > $o ).
thf(a_3_0_card_fil_decl,type,
a_3_0_card_fil: $i > $i > $i > $i ).
thf(k17_monoid_0_decl,type,
k17_monoid_0: $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(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_0_cantor_1_decl,type,
a_2_0_cantor_1: $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(k3_metric_1_decl,type,
k3_metric_1: $i ).
thf(k1_classes2_decl,type,
k1_classes2: $i > $i > $i ).
thf(f1_s3_funct_2_decl,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_decl,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_decl,type,
p1_s3_funct_2: $i > $i > $o ).
thf(k5_classes2_decl,type,
k5_classes2: $i > $i > $i > $i ).
thf(k2_finsub_1_decl,type,
k2_finsub_1: $i > $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(k5_funct_4_decl,type,
k5_funct_4: $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_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_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(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(m1_nat_lat_decl,type,
m1_nat_lat: $i > $i > $i > $i > $o ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k2_cqc_lang_decl,type,
k2_cqc_lang: $i > $i > $i > $i > $i > $i ).
thf(k13_mcart_1_decl,type,
k13_mcart_1: $i > $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(a_3_6_domain_1_decl,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(a_0_2_domain_1_decl,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_decl,type,
f3_s9_domain_1: $i ).
thf(k14_mcart_1_decl,type,
k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_0_0_domain_1_decl,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_decl,type,
f1_s7_domain_1: $i ).
thf(f1_s4_multop_1_decl,type,
f1_s4_multop_1: $i ).
thf(f2_s4_multop_1_decl,type,
f2_s4_multop_1: $i ).
thf(f3_s4_multop_1_decl,type,
f3_s4_multop_1: $i ).
thf(f4_s4_multop_1_decl,type,
f4_s4_multop_1: $i ).
thf(f5_s4_multop_1_decl,type,
f5_s4_multop_1: $i > $i > $i > $i ).
thf(f3_s11_funct_2_decl,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_decl,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_decl,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_decl,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_decl,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_decl,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_decl,type,
f7_s11_funct_2: $i > $i ).
thf(m1_pua2mss1_decl,type,
m1_pua2mss1: $i > $i > $i > $i > $o ).
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(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(r1_filter_2_decl,type,
r1_filter_2: $i > $i > $i > $o ).
thf(m1_triang_1_decl,type,
m1_triang_1: $i > $i > $i > $o ).
thf(p1_s6_domain_1_decl,type,
p1_s6_domain_1: $i > $o ).
thf(p2_s6_domain_1_decl,type,
p2_s6_domain_1: $i > $o ).
thf(a_1_5_domain_1_decl,type,
a_1_5_domain_1: $i > $i ).
thf(a_1_6_domain_1_decl,type,
a_1_6_domain_1: $i > $i ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
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(a_2_0_card_fil_decl,type,
a_2_0_card_fil: $i > $i > $i ).
thf(k5_trees_3_decl,type,
k5_trees_3: $i > $i ).
thf(a_1_3_domain_1_decl,type,
a_1_3_domain_1: $i > $i ).
thf(p1_s5_domain_1_decl,type,
p1_s5_domain_1: $i > $o ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
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(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(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(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(a_1_4_domain_1_decl,type,
a_1_4_domain_1: $i > $i ).
thf(p2_s5_domain_1_decl,type,
p2_s5_domain_1: $i > $o ).
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_s1_relset_1_decl,type,
f1_s1_relset_1: $i ).
thf(f2_s1_relset_1_decl,type,
f2_s1_relset_1: $i ).
thf(p1_s1_relset_1_decl,type,
p1_s1_relset_1: $i > $i > $o ).
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(k8_eqrel_1_decl,type,
k8_eqrel_1: $i > $i > $i ).
thf(a_3_4_domain_1_decl,type,
a_3_4_domain_1: $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(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(f1_s8_domain_1_decl,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_decl,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_decl,type,
p1_s8_domain_1: $i > $o ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
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_4_1_domain_1_decl,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
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(k9_domain_1_decl,type,
k9_domain_1: $i > $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(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(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(a_4_0_relset_2_decl,type,
a_4_0_relset_2: $i > $i > $i > $i > $i ).
thf(f1_s2_relset_1_decl,type,
f1_s2_relset_1: $i ).
thf(f2_s2_relset_1_decl,type,
f2_s2_relset_1: $i ).
thf(p1_s2_relset_1_decl,type,
p1_s2_relset_1: $i > $i > $o ).
thf(k2_classes2_decl,type,
k2_classes2: $i > $i > $i ).
thf(a_1_0_card_fil_decl,type,
a_1_0_card_fil: $i > $i ).
thf(a_3_8_domain_1_decl,type,
a_3_8_domain_1: $i > $i > $i > $i ).
thf(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(a_2_1_card_fil_decl,type,
a_2_1_card_fil: $i > $i > $i ).
thf(a_2_0_relset_2_decl,type,
a_2_0_relset_2: $i > $i > $i ).
thf(f1_s10_funct_2_decl,type,
f1_s10_funct_2: $i ).
thf(f2_s10_funct_2_decl,type,
f2_s10_funct_2: $i ).
thf(f3_s10_funct_2_decl,type,
f3_s10_funct_2: $i ).
thf(f4_s10_funct_2_decl,type,
f4_s10_funct_2: $i ).
thf(f5_s10_funct_2_decl,type,
f5_s10_funct_2: $i > $i ).
thf(p1_s3_domain_1_decl,type,
p1_s3_domain_1: $i > $i > $i > $o ).
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(f1_s2_pua2mss1_decl,type,
f1_s2_pua2mss1: $i ).
thf(f2_s2_pua2mss1_decl,type,
f2_s2_pua2mss1: $i ).
thf(p1_s2_pua2mss1_decl,type,
p1_s2_pua2mss1: $i > $i > $o ).
thf(p1_s10_fraenkel_decl,type,
p1_s10_fraenkel: $i > $o ).
thf(r1_cat_2_decl,type,
r1_cat_2: $i > $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(2432,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_4_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p2_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_4_domain_1) ).
thf(15170,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p2_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_4_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_4_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p2_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2432]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( 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(5857,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)],[615]) ).
thf(1882,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(12366,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)],[1882]) ).
thf(2550,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(15752,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)],[2550]) ).
thf(237,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(4022,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)],[237]) ).
thf(2473,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(15380,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)],[2473]) ).
thf(496,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(5385,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)],[496]) ).
thf(601,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(5810,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)],[601]) ).
thf(559,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(5659,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)],[559]) ).
thf(1447,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(9929,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)],[1447]) ).
thf(2100,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(13650,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)],[2100]) ).
thf(1148,axiom,
! [A: $i,B: $i,C: $i,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 ) )
=> ! [G: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( F @ ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ r2_hidden ) )
& ( E @ ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ r2_hidden ) )
& ( D @ ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_mcart_1) ).
thf(8536,plain,
! [A: $i,B: $i,C: $i,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 ) )
=> ! [G: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( F @ ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ r2_hidden ) )
& ( E @ ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ r2_hidden ) )
& ( D @ ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(568,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(5686,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)],[568]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = G ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_mcart_1) ).
thf(7304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = G ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1998,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(13052,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)],[1998]) ).
thf(2340,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_zfrefle1 ) )
=> ( A @ ( B @ r2_zfrefle1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_zfrefle1) ).
thf(14782,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_zfrefle1 ) )
=> ( A @ ( B @ r2_zfrefle1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340]) ).
thf(926,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(7427,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)],[926]) ).
thf(715,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(6387,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)],[715]) ).
thf(1081,axiom,
! [A: $i] :
( ( A @ k15_classes2 @ v1_classes2 )
& ~ ( A @ k15_classes2 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_classes2) ).
thf(8186,plain,
! [A: $i] :
( ( A @ k15_classes2 @ v1_classes2 )
& ~ ( A @ k15_classes2 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(719,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(6405,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)],[719]) ).
thf(2224,axiom,
? [A: $i] :
( ( A @ v1_fraenkel )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_fraenkel) ).
thf(14343,plain,
? [A: $i] :
( ( A @ v1_fraenkel )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( k1_xboole_0
!= ( C @ ( B @ ( A @ k11_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_finseq_3) ).
thf(4094,plain,
! [A: $i,B: $i,C: $i] :
( k1_xboole_0
!= ( C @ ( B @ ( A @ k11_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( E @ k2_mcart_1 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( E @ k1_mcart_1 @ k2_mcart_1 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( E @ k1_mcart_1 @ k1_mcart_1 @ k2_mcart_1 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( E @ k1_mcart_1 @ k1_mcart_1 @ k1_mcart_1 ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_mcart_1) ).
thf(5918,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( E @ k2_mcart_1 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( E @ k1_mcart_1 @ k2_mcart_1 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( E @ k1_mcart_1 @ k1_mcart_1 @ k2_mcart_1 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( E @ k1_mcart_1 @ k1_mcart_1 @ k1_mcart_1 ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1834,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(12055,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)],[1834]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ k19_mcart_1 )
= ( A @ k2_mcart_1 @ k1_mcart_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_mcart_1) ).
thf(2744,plain,
! [A: $i] :
( ( A @ k19_mcart_1 )
= ( A @ k2_mcart_1 @ k1_mcart_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1926,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(12607,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)],[1926]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ k1_enumset1 ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_enumset1) ).
thf(5593,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ k1_enumset1 ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(398,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(4909,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)],[398]) ).
thf(441,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(5136,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)],[441]) ).
thf(960,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(7569,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)],[960]) ).
thf(684,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(6231,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)],[684]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [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(2778,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)],[37]) ).
thf(2063,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(13402,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).
thf(1733,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(11372,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(2344,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_multop_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s4_multop_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f3_s4_multop_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( f4_s4_multop_1 @ ( f3_s4_multop_1 @ ( f2_s4_multop_1 @ ( f1_s4_multop_1 @ k2_multop_1 ) ) ) ) ) ) ) )
= ( D @ ( C @ ( B @ f5_s4_multop_1 ) ) ) ) ) ) )
& ( f4_s4_multop_1 @ ( f3_s4_multop_1 @ ( f2_s4_multop_1 @ ( f1_s4_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ m2_relset_1 ) ) )
& ( f4_s4_multop_1 @ ( f3_s4_multop_1 @ ( f2_s4_multop_1 @ ( f1_s4_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_multop_1) ).
thf(14801,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_multop_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s4_multop_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f3_s4_multop_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( f4_s4_multop_1 @ ( f3_s4_multop_1 @ ( f2_s4_multop_1 @ ( f1_s4_multop_1 @ k2_multop_1 ) ) ) ) ) ) ) )
= ( D @ ( C @ ( B @ f5_s4_multop_1 ) ) ) ) ) ) )
& ( f4_s4_multop_1 @ ( f3_s4_multop_1 @ ( f2_s4_multop_1 @ ( f1_s4_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ m2_relset_1 ) ) )
& ( f4_s4_multop_1 @ ( f3_s4_multop_1 @ ( f2_s4_multop_1 @ ( f1_s4_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344]) ).
thf(487,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(5329,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)],[487]) ).
thf(2369,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(14912,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369]) ).
thf(2241,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(14404,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)],[2241]) ).
thf(1143,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(8514,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)],[1143]) ).
thf(2258,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(14463,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)],[2258]) ).
thf(2492,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(15472,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)],[2492]) ).
thf(484,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(5320,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)],[484]) ).
thf(271,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(4183,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)],[271]) ).
thf(1597,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(10730,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)],[1597]) ).
thf(1689,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(11164,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)],[1689]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = H ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_mcart_1) ).
thf(7660,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = H ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = H ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(865,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(7100,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)],[865]) ).
thf(498,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(5390,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)],[498]) ).
thf(165,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(3581,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)],[165]) ).
thf(2203,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(14220,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)],[2203]) ).
thf(2290,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(14585,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)],[2290]) ).
thf(1601,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(10743,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)],[1601]) ).
thf(725,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(6431,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)],[725]) ).
thf(1264,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(9076,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)],[1264]) ).
thf(1221,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).
thf(8843,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(668,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(6121,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)],[668]) ).
thf(145,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(3449,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)],[145]) ).
thf(731,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(6448,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)],[731]) ).
thf(592,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(5778,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)],[592]) ).
thf(751,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 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(6555,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 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1806,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(11898,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)],[1806]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_tarski @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_tarski @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ k4_tarski ) @ ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_funct_1 ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_cat_1) ).
thf(9864,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_tarski @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_tarski @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ k4_tarski ) @ ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_funct_1 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(814,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(6845,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)],[814]) ).
thf(860,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(7072,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)],[860]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = I ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_mcart_1) ).
thf(6263,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = I ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(2479,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(15413,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)],[2479]) ).
thf(2228,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(14358,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)],[2228]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( ( A @ k2_mcart_1 )
= D )
| ( ( A @ k2_mcart_1 )
= C ) )
& ( ( A @ k1_mcart_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_mcart_1) ).
thf(4728,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( ( A @ k2_mcart_1 )
= D )
| ( ( A @ k2_mcart_1 )
= C ) )
& ( ( A @ k1_mcart_1 )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( D @ k2_mcart_1 ) )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( D @ k1_mcart_1 @ k2_mcart_1 ) )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( D @ k1_mcart_1 @ k1_mcart_1 ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_mcart_1) ).
thf(6954,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( D @ k2_mcart_1 ) )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( D @ k1_mcart_1 @ k2_mcart_1 ) )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( D @ k1_mcart_1 @ k1_mcart_1 ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(899,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(7285,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(389,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(4877,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)],[389]) ).
thf(2372,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k8_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_classes2) ).
thf(14932,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k8_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372]) ).
thf(1267,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(9091,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)],[1267]) ).
thf(1217,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(8828,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)],[1217]) ).
thf(1637,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(10901,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)],[1637]) ).
thf(1945,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_enumset1) ).
thf(12699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).
thf(1917,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(12507,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)],[1917]) ).
thf(1613,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(10790,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)],[1613]) ).
thf(1340,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(9437,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)],[1340]) ).
thf(1257,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relat_1) ).
thf(9032,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ k1_tarski @ ( A @ k2_xboole_0 ) ) )
=> ( C
= ( B @ ( C @ k1_funct_1 ) @ ( B @ k3_cqc_lang ) @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_7) ).
thf(6142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ k1_tarski @ ( A @ k2_xboole_0 ) ) )
=> ( C
= ( B @ ( C @ k1_funct_1 ) @ ( B @ k3_cqc_lang ) @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k2_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relset_2) ).
thf(7940,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k2_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1541,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(10431,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)],[1541]) ).
thf(81,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(3153,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)],[81]) ).
thf(1885,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_enumset1) ).
thf(12371,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).
thf(1594,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(10711,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)],[1594]) ).
thf(597,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(5793,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)],[597]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setwiseo) ).
thf(6602,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1667,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(11080,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)],[1667]) ).
thf(89,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(3185,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)],[89]) ).
thf(2392,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(15019,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)],[2392]) ).
thf(1903,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(12458,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)],[1903]) ).
thf(2469,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(15361,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)],[2469]) ).
thf(801,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(6791,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)],[801]) ).
thf(655,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(6063,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(2408,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k9_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_classes2) ).
thf(15066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k9_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2408]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( C @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( ( A @ k1_mcart_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_mcart_1) ).
thf(4037,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( C @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( ( A @ k1_mcart_1 )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(1985,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(12949,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)],[1985]) ).
thf(1614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( D @ ( B @ k1_tarski @ k2_funcop_1 ) @ ( C @ ( A @ k1_tarski @ k2_funcop_1 ) @ k1_funct_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_4) ).
thf(10795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( D @ ( B @ k1_tarski @ k2_funcop_1 ) @ ( C @ ( A @ k1_tarski @ k2_funcop_1 ) @ k1_funct_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(1828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k12_classes2 ) ) )
= ( C @ ( B @ k1_funct_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_classes2) ).
thf(12030,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k12_classes2 ) ) )
= ( C @ ( B @ k1_funct_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(7477,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1896,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(12426,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)],[1896]) ).
thf(2260,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(14468,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)],[2260]) ).
thf(1545,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(10446,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)],[1545]) ).
thf(1049,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(8044,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)],[1049]) ).
thf(913,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(7358,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)],[913]) ).
thf(827,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(6918,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(330,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(4500,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)],[330]) ).
thf(2299,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(14625,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)],[2299]) ).
thf(2325,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_classes2) ).
thf(14748,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325]) ).
thf(2326,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(14750,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)],[2326]) ).
thf(334,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(4515,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)],[334]) ).
thf(1938,axiom,
k1_xboole_0 @ k1_tarski @ ( k8_vectsp_2 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_vectsp_2) ).
thf(12666,plain,
k1_xboole_0 @ k1_tarski @ ( k8_vectsp_2 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938]) ).
thf(2524,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(15671,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)],[2524]) ).
thf(969,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(7641,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)],[969]) ).
thf(1385,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(9604,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)],[1385]) ).
thf(1586,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(10673,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)],[1586]) ).
thf(1887,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(12376,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)],[1887]) ).
thf(1327,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(9383,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)],[1327]) ).
thf(2555,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(15770,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)],[2555]) ).
thf(2423,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(15143,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423]) ).
thf(1444,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(9901,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)],[1444]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( A @ k2_mcart_1 )
= C )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_mcart_1) ).
thf(3285,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( A @ k2_mcart_1 )
= C )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(802,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(6798,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)],[802]) ).
thf(2308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_relset_1) ).
thf(14662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308]) ).
thf(1445,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(9918,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)],[1445]) ).
thf(1622,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k9_classes2 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_classes2) ).
thf(10837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k9_classes2 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(6776,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(2112,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ k2_ens_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k8_ens_1 ) )
<=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k2_ens_1 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k3_ens_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_ens_1) ).
thf(13707,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ k2_ens_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k2_ens_1 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k3_ens_1 ) ) ) )
=> ( B
= ( A @ k8_ens_1 ) ) )
& ( ( B
= ( A @ k8_ens_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k2_ens_1 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k3_ens_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112]) ).
thf(1518,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(10314,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)],[1518]) ).
thf(637,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(5982,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)],[637]) ).
thf(1262,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(9059,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(1076,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(8169,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)],[1076]) ).
thf(2595,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(15981,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)],[2595]) ).
thf(2083,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(13586,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)],[2083]) ).
thf(1976,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(12896,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)],[1976]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(5265,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(280,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(4215,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)],[280]) ).
thf(994,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(7781,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)],[994]) ).
thf(1378,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(9572,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)],[1378]) ).
thf(2442,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(15222,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)],[2442]) ).
thf(1333,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( A
= ( D @ ( C @ k2_xboole_0 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ r1_tarski ) ) )
=> ( E
= ( D @ ( E @ k7_relat_1 ) @ ( C @ ( E @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_sysrel) ).
thf(9400,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( A
= ( D @ ( C @ k2_xboole_0 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ r1_tarski ) ) )
=> ( E
= ( D @ ( E @ k7_relat_1 ) @ ( C @ ( E @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(408,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(4973,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)],[408]) ).
thf(2129,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(13845,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)],[2129]) ).
thf(2467,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(15346,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)],[2467]) ).
thf(530,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(5529,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)],[530]) ).
thf(2559,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(15780,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)],[2559]) ).
thf(1589,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_pboole) ).
thf(10694,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(552,axiom,
( ( k1_xboole_0 @ k4_card_3 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_card_3) ).
thf(5614,plain,
( ( k1_xboole_0 @ k4_card_3 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(2505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k2_cqc_lang ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_cqc_lang ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_cqc_lang) ).
thf(15579,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k2_cqc_lang ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_cqc_lang ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505]) ).
thf(1423,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(9818,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)],[1423]) ).
thf(1823,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(12013,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).
thf(785,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(6732,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)],[785]) ).
thf(1451,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(9950,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(523,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(5501,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)],[523]) ).
thf(1990,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_ens_1 ) )
= ( B @ k6_partfun1 @ ( B @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_ens_1) ).
thf(12971,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_ens_1 ) )
= ( B @ k6_partfun1 @ ( B @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).
thf(1453,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(9956,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)],[1453]) ).
thf(173,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(3648,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)],[173]) ).
thf(1025,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(7949,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)],[1025]) ).
thf(1949,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(12742,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)],[1949]) ).
thf(8,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(2627,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)],[8]) ).
thf(1319,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(9356,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)],[1319]) ).
thf(1569,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(10594,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)],[1569]) ).
thf(503,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(5412,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)],[503]) ).
thf(202,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(3794,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)],[202]) ).
thf(1394,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(9644,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)],[1394]) ).
thf(310,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( ( C @ ( A @ k4_finseq_2 ) )
= ( C @ ( B @ k4_finseq_2 ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_finseq_2) ).
thf(4403,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( ( C @ ( A @ k4_finseq_2 ) )
= ( C @ ( B @ k4_finseq_2 ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(142,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(3439,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)],[142]) ).
thf(2225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_enumset1) ).
thf(14347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225]) ).
thf(1983,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(12939,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)],[1983]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( E
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_mcart_1) ).
thf(6505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( E
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(2294,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(14602,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)],[2294]) ).
thf(1675,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(11112,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)],[1675]) ).
thf(67,axiom,
! [A: $i,B: $i] :
~ ( ~ ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( ( C
!= ( C @ k2_mcart_1 ) )
& ( C
!= ( C @ k1_mcart_1 ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_mcart_1) ).
thf(3049,plain,
! [A: $i,B: $i] :
~ ( ~ ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( ( C
!= ( C @ k2_mcart_1 ) )
& ( C
!= ( C @ k1_mcart_1 ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(194,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(3745,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)],[194]) ).
thf(1665,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(11072,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(1968,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_classes2 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_classes2) ).
thf(12852,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_classes2 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968]) ).
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(2607,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(2355,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_2) ).
thf(14856,plain,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355]) ).
thf(1173,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k12_ens_1 @ u1_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ens_1) ).
thf(8635,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k12_ens_1 @ u1_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(2390,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k3_classes2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_classes2) ).
thf(15013,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k3_classes2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390]) ).
thf(1487,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(10103,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)],[1487]) ).
thf(1157,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(8568,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)],[1157]) ).
thf(2274,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(14519,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)],[2274]) ).
thf(2118,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(13747,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)],[2118]) ).
thf(1260,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(9052,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)],[1260]) ).
thf(709,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(6359,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)],[709]) ).
thf(1524,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(10358,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)],[1524]) ).
thf(1842,axiom,
! [A: $i] :
( ( ( A @ v4_orders_3 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_orders_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_3) ).
thf(12126,plain,
! [A: $i] :
( ( ( A @ v4_orders_3 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_orders_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(1170,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( F @ m2_finseq_2 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( G @ m2_finseq_2 ) ) )
=> ( D @ ( A @ k4_finseq_2 ) @ ( D @ ( G @ ( F @ ( E @ k3_funcop_1 ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_finseq_2) ).
thf(8622,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( F @ m2_finseq_2 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( G @ m2_finseq_2 ) ) )
=> ( D @ ( A @ k4_finseq_2 ) @ ( D @ ( G @ ( F @ ( E @ k3_funcop_1 ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ k5_relat_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ ( B @ ( A @ k1_funct_1 ) @ k11_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_finseq_2) ).
thf(3044,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ k5_relat_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ ( B @ ( A @ k1_funct_1 ) @ k11_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1236,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(8913,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)],[1236]) ).
thf(951,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(7524,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)],[951]) ).
thf(669,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relat_1) ).
thf(6127,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(2005,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(13095,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)],[2005]) ).
thf(2210,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(14273,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)],[2210]) ).
thf(337,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(4528,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)],[337]) ).
thf(2316,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(14694,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)],[2316]) ).
thf(1699,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(11207,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ ( A @ k1_tarski @ m1_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(1302,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_xboole_1) ).
thf(9261,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(2458,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(15299,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)],[2458]) ).
thf(1144,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(8519,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)],[1144]) ).
thf(2588,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(15948,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)],[2588]) ).
thf(50,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(2933,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)],[50]) ).
thf(1421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_mcart_1) ).
thf(9813,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1819,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(11962,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)],[1819]) ).
thf(2450,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(15254,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)],[2450]) ).
thf(743,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(6515,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)],[743]) ).
thf(1356,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m4_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_realset1) ).
thf(9494,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m4_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(767,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(6634,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(659,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(6078,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)],[659]) ).
thf(1744,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(11513,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)],[1744]) ).
thf(446,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(5161,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)],[446]) ).
thf(2047,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(13298,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)],[2047]) ).
thf(2098,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(13640,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)],[2098]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_tarski ) @ k2_mcart_1 )
= B )
& ( ( B @ ( A @ k4_tarski ) @ k1_mcart_1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(3313,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_tarski ) @ k2_mcart_1 )
= B )
& ( ( B @ ( A @ k4_tarski ) @ k1_mcart_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ~ ( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_mcart_1) ).
thf(6336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ~ ( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(451,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(5178,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)],[451]) ).
thf(2511,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(15611,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)],[2511]) ).
thf(1177,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(8650,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)],[1177]) ).
thf(1230,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(8881,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)],[1230]) ).
thf(804,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(6804,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)],[804]) ).
thf(2475,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(15384,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)],[2475]) ).
thf(1537,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(10414,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)],[1537]) ).
thf(1297,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(9246,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)],[1297]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ~ ( A @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( A
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(7980,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ~ ( A @ ( D @ r2_hidden ) ) )
& ( ~ ( A @ ( D @ r2_hidden ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) ) )
=> ( A
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(2440,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(15207,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)],[2440]) ).
thf(410,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(4980,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)],[410]) ).
thf(2371,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(14927,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)],[2371]) ).
thf(2497,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(15514,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)],[2497]) ).
thf(2561,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(15791,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)],[2561]) ).
thf(1370,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(9540,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)],[1370]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(7220,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(874,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(7168,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)],[874]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(7018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(629,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(5935,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)],[629]) ).
thf(2459,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(15318,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)],[2459]) ).
thf(1289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k4_tarski ) @ ( C @ ( B @ k4_tarski ) @ ( D @ ( A @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_mcart_1) ).
thf(9195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k4_tarski ) @ ( C @ ( B @ k4_tarski ) @ ( D @ ( A @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(576,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(5723,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)],[576]) ).
thf(262,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(4137,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)],[262]) ).
thf(2029,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(13223,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)],[2029]) ).
thf(1795,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(11831,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)],[1795]) ).
thf(1496,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(10153,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)],[1496]) ).
thf(1450,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(9946,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)],[1450]) ).
thf(962,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(7605,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)],[962]) ).
thf(126,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(3370,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)],[126]) ).
thf(1771,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(11684,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)],[1771]) ).
thf(1235,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(8911,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)],[1235]) ).
thf(1690,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(11171,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)],[1690]) ).
thf(1737,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(11449,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)],[1737]) ).
thf(1584,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_finseq_2 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_finseq_2) ).
thf(10662,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) )
=> ( A @ ( B @ m1_finseq_2 ) ) )
& ( ( A @ ( B @ m1_finseq_2 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(6466,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(581,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(5740,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)],[581]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(7064,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(231,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(3994,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)],[231]) ).
thf(499,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(5393,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)],[499]) ).
thf(1059,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(8086,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)],[1059]) ).
thf(1431,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(9845,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)],[1431]) ).
thf(35,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(2763,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)],[35]) ).
thf(519,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 @ k5_xboole_0 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finsub_1) ).
thf(5486,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 @ k5_xboole_0 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1109,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(8325,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)],[1109]) ).
thf(2012,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(13127,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)],[2012]) ).
thf(1812,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(11930,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).
thf(1807,axiom,
! [A: $i] :
( ( A @ v1_setfam_1 )
<=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(11907,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)],[1807]) ).
thf(1773,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(11699,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(1214,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(8816,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(819,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(6887,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)],[819]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(8578,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1953,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(12763,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)],[1953]) ).
thf(1069,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(8133,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)],[1069]) ).
thf(1987,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(12960,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)],[1987]) ).
thf(1098,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(8256,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)],[1098]) ).
thf(1924,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(12543,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)],[1924]) ).
thf(2266,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(14488,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)],[2266]) ).
thf(2321,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(14716,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)],[2321]) ).
thf(2531,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(15688,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)],[2531]) ).
thf(792,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(6754,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(2220,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k1_classes2 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_classes2) ).
thf(14328,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k1_classes2 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220]) ).
thf(698,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(6306,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)],[698]) ).
thf(1044,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ k2_funct_5 )
= ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k2_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k1_funct_5 )
= ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_5) ).
thf(8025,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ k2_funct_5 )
= ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k2_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k1_funct_5 )
= ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(663,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(6102,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)],[663]) ).
thf(1725,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(11340,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)],[1725]) ).
thf(2303,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(14644,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303]) ).
thf(2410,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k4_classes2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_classes2) ).
thf(15077,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k4_classes2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2410]) ).
thf(289,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(4249,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)],[289]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(5342,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(2465,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(15342,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)],[2465]) ).
thf(778,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 @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_4) ).
thf(6707,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(2104,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(13664,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)],[2104]) ).
thf(2396,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(15033,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)],[2396]) ).
thf(184,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(3689,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)],[184]) ).
thf(1002,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(7822,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)],[1002]) ).
thf(19,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(2708,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)],[19]) ).
thf(473,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(5274,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)],[473]) ).
thf(706,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(6350,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)],[706]) ).
thf(2082,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(13553,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)],[2082]) ).
thf(572,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_zfmisc_1) ).
thf(5712,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(7386,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
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(12254,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(1167,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(8610,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)],[1167]) ).
thf(2271,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_enumset1) ).
thf(14510,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2271]) ).
thf(587,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(5765,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)],[587]) ).
thf(2368,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( A @ r3_zfrefle1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_zfrefle1) ).
thf(14909,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( A @ r3_zfrefle1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368]) ).
thf(1261,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(9056,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)],[1261]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finseq_1) ).
thf(4439,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(228,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(3976,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)],[228]) ).
thf(2194,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(14192,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)],[2194]) ).
thf(1643,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 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k8_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_domain_1) ).
thf(10935,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] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k8_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k8_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(2282,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(14552,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)],[2282]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(6892,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(544,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(5585,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)],[544]) ).
thf(219,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(3938,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)],[219]) ).
thf(1283,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(9172,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)],[1283]) ).
thf(1141,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(8500,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)],[1141]) ).
thf(299,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(4348,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)],[299]) ).
thf(1663,axiom,
! [A: $i] :
( ( ( A @ v5_grcat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_grcat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_grcat_1) ).
thf(11068,plain,
! [A: $i] :
( ( ( A @ v5_grcat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_grcat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(1908,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_enumset1) ).
thf(12475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).
thf(362,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(4743,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)],[362]) ).
thf(1018,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(7914,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)],[1018]) ).
thf(2107,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_realset1) ).
thf(13679,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).
thf(2261,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(14474,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)],[2261]) ).
thf(896,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(7277,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)],[896]) ).
thf(479,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(5306,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)],[479]) ).
thf(687,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(6242,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)],[687]) ).
thf(172,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(3644,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)],[172]) ).
thf(1578,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(10630,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)],[1578]) ).
thf(976,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 @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( B
= ( A @ k1_tarski @ ( C @ k2_xboole_0 ) ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( C @ ( A @ k8_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_yellow_9) ).
thf(7696,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 @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( B
= ( A @ k1_tarski @ ( C @ k2_xboole_0 ) ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( C @ ( A @ k8_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(2476,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(15387,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)],[2476]) ).
thf(17,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(2698,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)],[17]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ k18_mcart_1 )
= ( A @ k1_mcart_1 @ k2_mcart_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_mcart_1) ).
thf(3131,plain,
! [A: $i] :
( ( A @ k18_mcart_1 )
= ( A @ k1_mcart_1 @ k2_mcart_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(249,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(4070,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)],[249]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(8225,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1374,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k4_ens_1 ) )
= ( C @ ( A @ k3_ens_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_ens_1 ) ) )
= ( C @ k2_mcart_1 @ ( B @ k2_mcart_1 @ k5_relat_1 ) @ ( C @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ k4_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ens_1) ).
thf(9561,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k4_ens_1 ) )
= ( C @ ( A @ k3_ens_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_ens_1 ) ) )
= ( C @ k2_mcart_1 @ ( B @ k2_mcart_1 @ k5_relat_1 ) @ ( C @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ k4_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(1791,axiom,
! [A: $i] :
( ( A @ v1_setfam_1 )
=> ( A @ k2_yellow21 @ v4_orders_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow21) ).
thf(11817,plain,
! [A: $i] :
( ( A @ v1_setfam_1 )
=> ( A @ k2_yellow21 @ v4_orders_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(1459,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] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [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] :
( ( A @ ( H @ m2_finseq_1 ) )
=> ( ( H
= ( E @ ( D @ k10_finseq_1 ) ) )
=> ( ( F @ ( H @ ( G @ k4_funcop_1 ) ) )
= ( F @ ( E @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k10_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_finseq_2) ).
thf(9988,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] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [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] :
( ( A @ ( H @ m2_finseq_1 ) )
=> ( ( H
= ( E @ ( D @ k10_finseq_1 ) ) )
=> ( ( F @ ( H @ ( G @ k4_funcop_1 ) ) )
= ( F @ ( E @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k10_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1808,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(11913,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)],[1808]) ).
thf(1511,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(10251,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(2212,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(14277,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)],[2212]) ).
thf(1832,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(12046,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)],[1832]) ).
thf(2174,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(14088,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)],[2174]) ).
thf(953,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(7528,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)],[953]) ).
thf(1719,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(11299,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(957,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(7541,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)],[957]) ).
thf(1219,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(8834,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)],[1219]) ).
thf(2186,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 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k9_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_domain_1) ).
thf(14141,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] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k9_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k9_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186]) ).
thf(2251,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(14440,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)],[2251]) ).
thf(1211,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(8787,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)],[1211]) ).
thf(1692,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_enumset1) ).
thf(11178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(1145,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(8522,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)],[1145]) ).
thf(260,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(4130,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)],[260]) ).
thf(701,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(6315,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)],[701]) ).
thf(2124,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(13776,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)],[2124]) ).
thf(1055,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(8069,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)],[1055]) ).
thf(2478,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(15394,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)],[2478]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ k3_enumset1 ) ) ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_enumset1) ).
thf(7867,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ k3_enumset1 ) ) ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1790,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(11812,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)],[1790]) ).
thf(779,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(6713,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)],[779]) ).
thf(1418,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k9_funct_2 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k3_cqc_lang ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_cqc_lang) ).
thf(9805,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k9_funct_2 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k3_cqc_lang ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(1398,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(9668,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)],[1398]) ).
thf(2238,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ v4_finsub_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(14391,plain,
! [A: $i] : ( A @ k5_finsub_1 @ v4_finsub_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_mcart_1) ).
thf(5989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1043,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(8022,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(2040,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(13273,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)],[2040]) ).
thf(2587,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(15943,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)],[2587]) ).
thf(204,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(3803,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)],[204]) ).
thf(1759,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(11628,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( k9_zf_lang @ k1_subset_1 @ ( A @ r1_zfrefle1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(1095,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(8242,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)],[1095]) ).
thf(316,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(4428,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)],[316]) ).
thf(2205,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(14228,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)],[2205]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_relat_1) ).
thf(3713,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(288,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(4243,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)],[288]) ).
thf(670,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] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [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] :
( ( B @ ( H @ m2_finseq_1 ) )
=> ( ( H
= ( F @ ( E @ k10_finseq_1 ) ) )
=> ( ( H @ ( D @ ( G @ k5_funcop_1 ) ) )
= ( F @ ( D @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k10_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_finseq_2) ).
thf(6130,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] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [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] :
( ( B @ ( H @ m2_finseq_1 ) )
=> ( ( H
= ( F @ ( E @ k10_finseq_1 ) ) )
=> ( ( H @ ( D @ ( G @ k5_funcop_1 ) ) )
= ( F @ ( D @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( G @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k10_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1781,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_1) ).
thf(11760,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(2156,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(14002,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)],[2156]) ).
thf(2221,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(14331,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)],[2221]) ).
thf(740,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(6502,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)],[740]) ).
thf(2060,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(13388,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)],[2060]) ).
thf(293,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(4265,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)],[293]) ).
thf(2568,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(15824,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)],[2568]) ).
thf(323,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(4471,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)],[323]) ).
thf(1935,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(12657,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)],[1935]) ).
thf(2437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(15199,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437]) ).
thf(1950,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(12745,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)],[1950]) ).
thf(582,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( k1_numbers @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_membered) ).
thf(5744,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( k1_numbers @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1392,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(9629,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)],[1392]) ).
thf(15,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(2691,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)],[15]) ).
thf(148,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(3463,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)],[148]) ).
thf(1162,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_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_4) ).
thf(8590,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_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1416,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(9800,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)],[1416]) ).
thf(1821,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(11981,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)],[1821]) ).
thf(467,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(5256,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)],[467]) ).
thf(1557,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(10534,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)],[1557]) ).
thf(48,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(2857,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)],[48]) ).
thf(1738,axiom,
( ! [A: $i] :
( ( f1_s2_multop_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_multop_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_multop_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ ( A @ p1_s2_multop_1 ) ) ) )
& ( f1_s2_multop_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_multop_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_multop_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f1_s2_multop_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ k2_multop_1 ) ) ) ) ) ) ) @ ( D @ ( C @ ( B @ p1_s2_multop_1 ) ) ) ) ) ) )
& ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ m2_relset_1 ) ) )
& ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_multop_1) ).
thf(11463,plain,
( ! [A: $i] :
( ( f1_s2_multop_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_multop_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_multop_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ ( A @ p1_s2_multop_1 ) ) ) )
& ( f1_s2_multop_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_multop_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_multop_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f1_s2_multop_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ k2_multop_1 ) ) ) ) ) ) ) @ ( D @ ( C @ ( B @ p1_s2_multop_1 ) ) ) ) ) ) )
& ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ m2_relset_1 ) ) )
& ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ ( f1_s2_multop_1 @ k3_zfmisc_1 ) ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(618,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(5866,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)],[618]) ).
thf(737,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(6470,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)],[737]) ).
thf(456,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(5214,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)],[456]) ).
thf(2232,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(14376,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)],[2232]) ).
thf(373,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_ens_1 ) )
= ( B @ k1_mcart_1 @ k2_mcart_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_ens_1) ).
thf(4788,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_ens_1 ) )
= ( B @ k1_mcart_1 @ k2_mcart_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1588,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(10687,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)],[1588]) ).
thf(1232,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(8902,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)],[1232]) ).
thf(171,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(3638,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)],[171]) ).
thf(527,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(5521,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)],[527]) ).
thf(824,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(6905,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)],[824]) ).
thf(2199,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(14205,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)],[2199]) ).
thf(2256,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_finsub_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
thf(14455,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_finsub_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256]) ).
thf(718,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(6396,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)],[718]) ).
thf(1673,axiom,
~ ( k1_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_numbers) ).
thf(11100,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(599,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(5802,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)],[599]) ).
thf(1281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ~ ( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_mcart_1) ).
thf(9155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ~ ( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(998,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ k12_ens_1 @ u1_cat_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ens_1) ).
thf(7803,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ k12_ens_1 @ u1_cat_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1215,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(8819,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1196,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(8717,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)],[1196]) ).
thf(2337,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(14773,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m2_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2337]) ).
thf(1430,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(9843,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)],[1430]) ).
thf(1846,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(12137,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)],[1846]) ).
thf(757,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(6579,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)],[757]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = J ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_mcart_1) ).
thf(8468,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = J ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1867,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(12269,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)],[1867]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(5622,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 @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_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)],[555]) ).
thf(485,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(5323,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)],[485]) ).
thf(402,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(4928,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)],[402]) ).
thf(381,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(4830,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)],[381]) ).
thf(1930,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_partfun1 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_partfun1) ).
thf(12621,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_partfun1 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).
thf(799,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [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 @ ( B @ ( A @ r2_realset1 ) ) )
<=> ( ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_2 ) ) )
& ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ m1_realset1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_realset1) ).
thf(6781,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [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 @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_2 ) ) )
& ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ m1_realset1 ) ) ) )
=> ( C @ ( B @ ( A @ r2_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_realset1 ) ) )
=> ( ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_2 ) ) )
& ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ m1_realset1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1861,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(12229,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)],[1861]) ).
thf(828,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(6923,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1678,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(11132,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)],[1678]) ).
thf(1852,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(12180,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)],[1852]) ).
thf(613,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(5851,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)],[613]) ).
thf(1321,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(9362,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)],[1321]) ).
thf(606,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(5829,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)],[606]) ).
thf(2292,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(14597,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)],[2292]) ).
thf(1295,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(9240,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)],[1295]) ).
thf(583,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(5746,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)],[583]) ).
thf(2530,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(15684,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)],[2530]) ).
thf(1455,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(9973,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)],[1455]) ).
thf(189,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(3708,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)],[189]) ).
thf(2376,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(14949,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2376]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
& ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( C @ ( B @ ( A @ k6_ens_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_ens_1) ).
thf(5076,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
& ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( C @ ( B @ ( A @ k6_ens_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(2037,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(13263,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)],[2037]) ).
thf(2053,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(13350,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)],[2053]) ).
thf(98,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(3231,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)],[98]) ).
thf(1818,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(11959,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)],[1818]) ).
thf(1096,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(8252,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(2050,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A
= ( C @ k1_tarski ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_pua2mss1) ).
thf(13332,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( A
= ( C @ k1_tarski ) )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A
= ( C @ k1_tarski ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).
thf(713,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(6382,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)],[713]) ).
thf(104,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(3258,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)],[104]) ).
thf(1919,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(12517,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).
thf(1304,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(9266,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(1226,axiom,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_5) ).
thf(8870,plain,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(986,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(7733,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)],[986]) ).
thf(885,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(7236,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)],[885]) ).
thf(2015,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_partfun1 ) @ ( A @ ( C @ k4_partfun1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_partfun1) ).
thf(13134,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_partfun1 ) @ ( A @ ( C @ k4_partfun1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(366,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(4756,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)],[366]) ).
thf(884,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(7226,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)],[884]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k4_tarski ) @ ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_funct_1 ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_cat_1) ).
thf(8956,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k4_tarski ) @ ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_funct_1 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(396,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(4903,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)],[396]) ).
thf(419,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(5027,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)],[419]) ).
thf(1717,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(11293,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)],[1717]) ).
thf(822,axiom,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(6895,plain,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(2280,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(14547,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)],[2280]) ).
thf(1668,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_partfun1 ) @ ( A @ ( k1_xboole_0 @ k4_partfun1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_partfun1) ).
thf(11083,plain,
! [A: $i,B: $i] : ( A @ ( B @ k4_partfun1 ) @ ( A @ ( k1_xboole_0 @ k4_partfun1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(848,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(7015,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)],[848]) ).
thf(1393,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(9636,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)],[1393]) ).
thf(2415,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(15105,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)],[2415]) ).
thf(1793,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(11821,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)],[1793]) ).
thf(1309,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(9298,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)],[1309]) ).
thf(1539,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(10419,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)],[1539]) ).
thf(2495,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(15500,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)],[2495]) ).
thf(1825,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(12018,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)],[1825]) ).
thf(812,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(6840,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)],[812]) ).
thf(1979,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(12924,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)],[1979]) ).
thf(1602,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(10746,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)],[1602]) ).
thf(1785,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(11778,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(226,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(3966,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)],[226]) ).
thf(1765,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k2_ens_1 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k2_ens_1 @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k11_ens_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_ens_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k5_ens_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_ens_1) ).
thf(11656,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k2_ens_1 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k2_ens_1 @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_ens_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k5_ens_1 ) ) ) )
=> ( B
= ( A @ k11_ens_1 ) ) )
& ( ( B
= ( A @ k11_ens_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_ens_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k5_ens_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ ( D @ ( C @ k1_enumset1 ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_enumset1) ).
thf(7894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ ( D @ ( C @ k1_enumset1 ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(2540,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(15716,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)],[2540]) ).
thf(529,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(5526,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1439,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(9882,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)],[1439]) ).
thf(268,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(4173,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)],[268]) ).
thf(1575,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(10623,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)],[1575]) ).
thf(53,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(2996,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)],[53]) ).
thf(888,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(7245,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)],[888]) ).
thf(1568,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(10591,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)],[1568]) ).
thf(178,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(3670,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)],[178]) ).
thf(2117,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_partfun1 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_partfun1) ).
thf(13744,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_partfun1 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117]) ).
thf(917,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(7369,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)],[917]) ).
thf(2549,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k8_classes2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k8_classes2) ).
thf(15748,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k8_classes2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2549]) ).
thf(1805,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(11891,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)],[1805]) ).
thf(930,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(7441,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)],[930]) ).
thf(745,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(6523,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)],[745]) ).
thf(2449,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(15246,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)],[2449]) ).
thf(992,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(7775,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1212,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(8791,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)],[1212]) ).
thf(1420,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_mcart_1) ).
thf(9811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(5680,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(789,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(6745,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)],[789]) ).
thf(2513,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k4_finsub_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_finsub_1) ).
thf(15623,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k4_finsub_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2513]) ).
thf(1702,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(11215,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)],[1702]) ).
thf(678,axiom,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(6176,plain,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(227,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(3973,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)],[227]) ).
thf(1797,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(11838,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)],[1797]) ).
thf(2425,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(15150,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)],[2425]) ).
thf(1180,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(8659,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)],[1180]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != C )
=> ( ( D @ ( B @ ( C @ ( A @ k4_funct_4 ) ) ) )
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_4) ).
thf(8018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != C )
=> ( ( D @ ( B @ ( C @ ( A @ k4_funct_4 ) ) ) )
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(600,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(5805,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)],[600]) ).
thf(481,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(5311,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)],[481]) ).
thf(638,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] :
( ( 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 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( J @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( J @ v1_funct_2 ) ) )
& ( J @ v1_funct_1 ) )
=> ! [K: $i] :
( ( A @ ( K @ m2_finseq_1 ) )
=> ! [L: $i] :
( ( B @ ( L @ m2_finseq_1 ) )
=> ( ( ( L
= ( I @ ( H @ ( G @ k11_finseq_1 ) ) ) )
& ( K
= ( F @ ( E @ ( D @ k11_finseq_1 ) ) ) ) )
=> ( ( L @ ( K @ ( J @ k3_funcop_1 ) ) )
= ( I @ ( F @ ( J @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( H @ ( E @ ( J @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( J @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_finseq_2) ).
thf(5985,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] :
( ( 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 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( J @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( J @ v1_funct_2 ) ) )
& ( J @ v1_funct_1 ) )
=> ! [K: $i] :
( ( A @ ( K @ m2_finseq_1 ) )
=> ! [L: $i] :
( ( B @ ( L @ m2_finseq_1 ) )
=> ( ( ( L
= ( I @ ( H @ ( G @ k11_finseq_1 ) ) ) )
& ( K
= ( F @ ( E @ ( D @ k11_finseq_1 ) ) ) ) )
=> ( ( L @ ( K @ ( J @ k3_funcop_1 ) ) )
= ( I @ ( F @ ( J @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( H @ ( E @ ( J @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( J @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(110,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(3290,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)],[110]) ).
thf(1788,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(11793,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)],[1788]) ).
thf(2593,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k8_classes2 ) ) )
= ( B @ ( C @ ( A @ k8_classes2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k8_classes2) ).
thf(15975,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k8_classes2 ) ) )
= ( B @ ( C @ ( A @ k8_classes2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2593]) ).
thf(69,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(3093,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)],[69]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = J ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_mcart_1) ).
thf(6823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = J ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = J ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
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 ) )
<=> ( ( 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(11708,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)],[1775]) ).
thf(1204,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(8759,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1820,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(11971,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)],[1820]) ).
thf(2089,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(13604,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)],[2089]) ).
thf(2236,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(14387,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)],[2236]) ).
thf(727,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(6438,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)],[727]) ).
thf(1598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_partfun1) ).
thf(10734,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(468,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(5259,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)],[468]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(8196,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(2572,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(15834,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)],[2572]) ).
thf(1571,axiom,
! [A: $i] :
( ( ( A @ v2_cat_5 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_cat_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_cat_5) ).
thf(10602,plain,
! [A: $i] :
( ( ( A @ v2_cat_5 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_cat_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(213,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(3851,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)],[213]) ).
thf(425,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(5059,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)],[425]) ).
thf(1036,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(8001,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)],[1036]) ).
thf(62,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(3036,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)],[62]) ).
thf(2164,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(14046,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)],[2164]) ).
thf(937,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(7473,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)],[937]) ).
thf(627,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(5929,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(354,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(4718,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)],[354]) ).
thf(2214,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(14284,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)],[2214]) ).
thf(2538,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(15712,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)],[2538]) ).
thf(2537,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(15710,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)],[2537]) ).
thf(1723,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(11312,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)],[1723]) ).
thf(853,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(7036,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)],[853]) ).
thf(1585,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k8_classes2 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_classes2) ).
thf(10670,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k8_classes2 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(1934,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(12638,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)],[1934]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_mcart_1) ).
thf(5773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(2435,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(15186,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)],[2435]) ).
thf(493,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(5353,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)],[493]) ).
thf(1389,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(9616,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)],[1389]) ).
thf(385,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(4842,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)],[385]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(8454,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(2230,axiom,
! [A: $i] : ( A @ k6_lattice5 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice5) ).
thf(14372,plain,
! [A: $i] : ( A @ k6_lattice5 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230]) ).
thf(1322,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(9369,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)],[1322]) ).
thf(2490,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(15458,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)],[2490]) ).
thf(787,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(6740,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1562,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 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k11_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = J ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_domain_1) ).
thf(10551,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] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = J ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k11_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k11_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = J ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(2146,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(13938,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)],[2146]) ).
thf(1620,axiom,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k12_ens_1 @ u2_cat_1 @ ( B @ ( A @ k15_ens_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_ens_1) ).
thf(10833,plain,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k12_ens_1 @ u2_cat_1 @ ( B @ ( A @ k15_ens_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1000,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(7807,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)],[1000]) ).
thf(1961,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(12824,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)],[1961]) ).
thf(2359,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(14874,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)],[2359]) ).
thf(909,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] : ( A @ ( B @ m4_realset1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m4_realset1) ).
thf(7336,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] : ( A @ ( B @ m4_realset1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(331,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(4504,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)],[331]) ).
thf(2556,axiom,
k9_zf_lang @ k1_zfmisc_1 @ ( k2_zfrefle1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfrefle1) ).
thf(15774,plain,
k9_zf_lang @ k1_zfmisc_1 @ ( k2_zfrefle1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2556]) ).
thf(1016,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(7909,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)],[1016]) ).
thf(2388,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k13_ens_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_ens_1) ).
thf(15008,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k13_ens_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388]) ).
thf(2571,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(15831,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)],[2571]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(6347,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(464,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(5246,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)],[464]) ).
thf(296,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(4307,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1115,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(8347,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)],[1115]) ).
thf(1027,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(7954,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)],[1027]) ).
thf(1915,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(12499,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)],[1915]) ).
thf(1258,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(9035,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)],[1258]) ).
thf(1474,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(10057,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)],[1474]) ).
thf(624,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(5897,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)],[624]) ).
thf(1892,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(12411,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)],[1892]) ).
thf(1188,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(8691,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)],[1188]) ).
thf(125,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(3361,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)],[125]) ).
thf(197,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(3756,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)],[197]) ).
thf(42,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(2809,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)],[42]) ).
thf(1488,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(10106,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)],[1488]) ).
thf(40,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(2799,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)],[40]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( k1_xboole_0
!= ( B @ ( A @ k10_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_finseq_3) ).
thf(2639,plain,
! [A: $i,B: $i] :
( k1_xboole_0
!= ( B @ ( A @ k10_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1648,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(10977,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)],[1648]) ).
thf(2342,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(14798,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342]) ).
thf(1971,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(12860,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)],[1971]) ).
thf(2546,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(15738,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)],[2546]) ).
thf(2468,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(15350,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)],[2468]) ).
thf(1642,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(10932,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)],[1642]) ).
thf(702,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(6327,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)],[702]) ).
thf(1129,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(8443,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)],[1129]) ).
thf(1682,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(11143,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)],[1682]) ).
thf(352,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(4707,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)],[352]) ).
thf(167,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(3588,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)],[167]) ).
thf(393,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_pua2mss1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).
thf(4892,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_pua2mss1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(945,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(7505,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_tarski @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(2460,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(15321,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)],[2460]) ).
thf(2374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k5_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_classes2) ).
thf(14945,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k5_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(7688,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(605,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(5824,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)],[605]) ).
thf(1306,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(9272,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)],[1306]) ).
thf(1045,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 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_domain_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_domain_1) ).
thf(8033,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 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_domain_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(22,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(2718,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)],[22]) ).
thf(132,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(3406,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)],[132]) ).
thf(634,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(5970,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)],[634]) ).
thf(1381,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(9584,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(1468,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(10029,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)],[1468]) ).
thf(1105,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(8289,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)],[1105]) ).
thf(158,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(3510,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)],[158]) ).
thf(248,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(4065,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)],[248]) ).
thf(569,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(5695,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)],[569]) ).
thf(1238,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(8924,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)],[1238]) ).
thf(2446,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(15235,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)],[2446]) ).
thf(2196,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(14196,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)],[2196]) ).
thf(1341,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(9440,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)],[1341]) ).
thf(170,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(3635,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)],[170]) ).
thf(1748,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(11545,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)],[1748]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(5298,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1068,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(8123,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)],[1068]) ).
thf(141,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
~ ( ( A
!= ( B @ ( C @ k10_finseq_1 ) ) )
& ( A
!= ( C @ ( B @ k10_finseq_1 ) ) )
& ( B != C )
& ( ( A @ k2_relat_1 )
= ( C @ ( B @ k2_tarski ) ) )
& ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_finseq_3) ).
thf(3435,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
~ ( ( A
!= ( B @ ( C @ k10_finseq_1 ) ) )
& ( A
!= ( C @ ( B @ k10_finseq_1 ) ) )
& ( B != C )
& ( ( A @ k2_relat_1 )
= ( C @ ( B @ k2_tarski ) ) )
& ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1769,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k1_finsub_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_finsub_1) ).
thf(11677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k1_finsub_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(2168,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(14060,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)],[2168]) ).
thf(1203,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(8751,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)],[1203]) ).
thf(1982,axiom,
? [A: $i] :
( ( A @ v4_orders_3 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_orders_3) ).
thf(12935,plain,
? [A: $i] :
( ( A @ v4_orders_3 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).
thf(1756,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(11597,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)],[1756]) ).
thf(2192,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(14184,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)],[2192]) ).
thf(1687,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(11159,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(1350,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_cqc_lang ) @ v1_funct_1 )
& ( B @ ( A @ k3_cqc_lang ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_cqc_lang) ).
thf(9472,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_cqc_lang ) @ v1_funct_1 )
& ( B @ ( A @ k3_cqc_lang ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(2076,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( C @ ( D @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_enumset1) ).
thf(13526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( C @ ( D @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = F ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_mcart_1) ).
thf(7197,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = F ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = F ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(449,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(5174,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)],[449]) ).
thf(631,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(5961,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)],[631]) ).
thf(2105,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(13671,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)],[2105]) ).
thf(2140,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(13885,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)],[2140]) ).
thf(2043,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(13286,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)],[2043]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(7254,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(2322,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(14730,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)],[2322]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_enumset1) ).
thf(7535,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(746,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(6529,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)],[746]) ).
thf(2278,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(14537,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)],[2278]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ k1_tarski @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_enumset1) ).
thf(10725,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ k1_tarski @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(2252,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(14445,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252]) ).
thf(214,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ m2_finseq_2 ) ) )
=> ! [D: $i] :
( ( ( A @ k2_finseq_1 @ ( A @ k2_finseq_1 @ ( D @ m2_relset_1 ) ) )
& ( A @ k2_finseq_1 @ ( A @ k2_finseq_1 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ k2_relat_1 )
= ( A @ k2_finseq_1 ) )
=> ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ ( D @ ( B @ ( k5_numbers @ ( A @ k2_finseq_1 @ ( A @ k2_finseq_1 @ k1_partfun1 ) ) ) ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_finseq_2) ).
thf(3857,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ m2_finseq_2 ) ) )
=> ! [D: $i] :
( ( ( A @ k2_finseq_1 @ ( A @ k2_finseq_1 @ ( D @ m2_relset_1 ) ) )
& ( A @ k2_finseq_1 @ ( A @ k2_finseq_1 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ k2_relat_1 )
= ( A @ k2_finseq_1 ) )
=> ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ ( D @ ( B @ ( k5_numbers @ ( A @ k2_finseq_1 @ ( A @ k2_finseq_1 @ k1_partfun1 ) ) ) ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(794,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(6760,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)],[794]) ).
thf(276,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(4199,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)],[276]) ).
thf(1617,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(10811,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)],[1617]) ).
thf(2059,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(13386,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)],[2059]) ).
thf(1838,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(12078,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)],[1838]) ).
thf(113,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(3303,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)],[113]) ).
thf(406,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(4962,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)],[406]) ).
thf(2351,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(14836,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)],[2351]) ).
thf(1175,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(8640,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)],[1175]) ).
thf(2130,axiom,
! [A: $i] :
( ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ k2_zfmisc_1 ) @ ( A @ k17_monoid_0 @ m2_relset_1 ) ) )
& ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ k2_zfmisc_1 ) @ ( A @ k17_monoid_0 @ v1_funct_2 ) ) )
& ( A @ k17_monoid_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_monoid_0) ).
thf(13848,plain,
! [A: $i] :
( ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ k2_zfmisc_1 ) @ ( A @ k17_monoid_0 @ m2_relset_1 ) ) )
& ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ ( A @ ( A @ k4_partfun1 ) @ k2_zfmisc_1 ) @ ( A @ k17_monoid_0 @ v1_funct_2 ) ) )
& ( A @ k17_monoid_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ k2_mcart_1 )
= ( D @ k2_mcart_1 ) )
& ( ( C @ k1_mcart_1 )
= ( D @ k1_mcart_1 ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_domain_1) ).
thf(3567,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ k2_mcart_1 )
= ( D @ k2_mcart_1 ) )
& ( ( C @ k1_mcart_1 )
= ( D @ k1_mcart_1 ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(850,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(7022,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)],[850]) ).
thf(1645,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 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k10_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = I ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_domain_1) ).
thf(10954,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] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = I ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k10_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k10_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = I ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(1239,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(8927,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)],[1239]) ).
thf(1094,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(8233,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)],[1094]) ).
thf(988,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(7745,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)],[988]) ).
thf(230,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(3984,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)],[230]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k3_cqc_lang ) @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( B @ ( A @ k3_cqc_lang ) @ k1_relat_1 )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_cqc_lang) ).
thf(3169,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k3_cqc_lang ) @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( B @ ( A @ k3_cqc_lang ) @ k1_relat_1 )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(106,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(3265,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)],[106]) ).
thf(1787,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(11791,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(1428,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(9836,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)],[1428]) ).
thf(1249,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_membered )
& ( A @ v1_membered ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_membered) ).
thf(9004,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_membered )
& ( A @ v1_membered ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(338,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(4531,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)],[338]) ).
thf(1118,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(8365,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)],[1118]) ).
thf(2483,axiom,
? [A: $i] :
( ( A @ v5_grcat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_grcat_1) ).
thf(15424,plain,
? [A: $i] :
( ( A @ v5_grcat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483]) ).
thf(2433,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k4_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_urysohn1) ).
thf(15179,plain,
k1_numbers @ k1_zfmisc_1 @ ( k4_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433]) ).
thf(1878,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(12350,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)],[1878]) ).
thf(2486,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_partfun1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pua2mss1) ).
thf(15449,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_partfun1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486]) ).
thf(654,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(6058,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)],[654]) ).
thf(633,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(5968,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(2529,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(15682,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)],[2529]) ).
thf(536,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(5545,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)],[536]) ).
thf(2049,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(13322,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)],[2049]) ).
thf(1415,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setwiseo) ).
thf(9797,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(2138,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(13875,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)],[2138]) ).
thf(2534,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(15697,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2534]) ).
thf(442,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ? [B: $i] :
( ( A @ ( B @ v3_card_fil ) )
& ~ ( A @ ( B @ v2_card_fil ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_card_fil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_fil) ).
thf(5142,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ? [B: $i] :
( ( A @ ( B @ v3_card_fil ) )
& ~ ( A @ ( B @ v2_card_fil ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_card_fil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(340,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(4557,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)],[340]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(7937,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(2030,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(13233,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)],[2030]) ).
thf(1242,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(8959,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)],[1242]) ).
thf(2583,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(15920,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)],[2583]) ).
thf(1168,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(8613,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)],[1168]) ).
thf(541,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(5562,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)],[541]) ).
thf(1640,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(10922,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)],[1640]) ).
thf(2209,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_2_ens_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ( B @ k7_ens_1 ) ) ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_2_ens_1) ).
thf(14263,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ( B @ k7_ens_1 ) ) ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_2_ens_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_2_ens_1 @ ( A @ r2_hidden ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ( B @ k7_ens_1 ) ) ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2209]) ).
thf(2553,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(15766,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)],[2553]) ).
thf(1639,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(10911,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)],[1639]) ).
thf(2477,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(15392,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)],[2477]) ).
thf(2452,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(15258,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)],[2452]) ).
thf(343,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(4576,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)],[343]) ).
thf(1844,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(12132,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)],[1844]) ).
thf(1996,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k2_zfmisc_1 ) @ ( A @ k10_ens_1 @ m2_relset_1 ) ) )
& ( A @ k10_ens_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_ens_1) ).
thf(12985,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k2_zfmisc_1 ) @ ( A @ k10_ens_1 @ m2_relset_1 ) ) )
& ( A @ k10_ens_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).
thf(818,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(6884,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)],[818]) ).
thf(1172,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(8630,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)],[1172]) ).
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 ) )
=> ! [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(4031,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)],[239]) ).
thf(297,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(4312,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)],[297]) ).
thf(1837,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(12073,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)],[1837]) ).
thf(2345,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_yellow21 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow21) ).
thf(14808,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_yellow21 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2345]) ).
thf(2499,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(15518,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)],[2499]) ).
thf(1035,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(7999,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)],[1035]) ).
thf(1284,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(9175,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)],[1284]) ).
thf(1314,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(9323,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)],[1314]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( A @ ( C @ ( B @ k10_finseq_1 ) @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finseq_2) ).
thf(3418,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( A @ ( C @ ( B @ k10_finseq_1 ) @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1628,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(10855,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)],[1628]) ).
thf(868,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(7110,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)],[868]) ).
thf(1591,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(10699,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)],[1591]) ).
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(12664,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(1624,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(10843,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)],[1624]) ).
thf(1666,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(11074,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)],[1666]) ).
thf(120,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(3339,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)],[120]) ).
thf(2080,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_enumset1) ).
thf(13547,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).
thf(1271,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(9105,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)],[1271]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_cat_1 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k3_cqc_lang ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cat_1) ).
thf(7730,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_cat_1 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k3_cqc_lang ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1113,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(8343,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)],[1113]) ).
thf(1898,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_finsub_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
thf(12437,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_finsub_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).
thf(1486,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(10099,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)],[1486]) ).
thf(105,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(3261,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)],[105]) ).
thf(353,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(4712,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)],[353]) ).
thf(1753,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(11582,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)],[1753]) ).
thf(1890,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(12385,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)],[1890]) ).
thf(551,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(5611,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)],[551]) ).
thf(855,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(7042,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(1210,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(8783,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)],[1210]) ).
thf(1724,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(11339,plain,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k4_qc_lang1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(1927,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(12613,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)],[1927]) ).
thf(823,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(6897,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)],[823]) ).
thf(1363,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ k2_tarski ) @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_enumset1) ).
thf(9522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ k2_tarski ) @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(190,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(3711,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)],[190]) ).
thf(1707,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 @ ( A @ ( A @ k11_ens_1 @ m2_relset_1 ) ) )
& ( A @ k2_ens_1 @ ( A @ ( A @ k11_ens_1 @ v1_funct_2 ) ) )
& ( A @ k11_ens_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_ens_1) ).
thf(11238,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 @ ( A @ ( A @ k11_ens_1 @ m2_relset_1 ) ) )
& ( A @ k2_ens_1 @ ( A @ ( A @ k11_ens_1 @ v1_funct_2 ) ) )
& ( A @ k11_ens_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1004,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(7870,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)],[1004]) ).
thf(235,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(4016,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)],[235]) ).
thf(1501,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(10171,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)],[1501]) ).
thf(2544,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(15734,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)],[2544]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = H ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_mcart_1) ).
thf(6000,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = H ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(2573,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(15843,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)],[2573]) ).
thf(2333,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(14766,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)],[2333]) ).
thf(1,conjecture,
! [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(2,negated_conjecture,
~ ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(2596,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)],[2]) ).
thf(218,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(3867,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)],[218]) ).
thf(1647,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).
thf(10975,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(1658,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(11037,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)],[1658]) ).
thf(2485,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(15434,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)],[2485]) ).
thf(796,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(6773,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)],[796]) ).
thf(543,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(5579,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)],[543]) ).
thf(525,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(5512,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)],[525]) ).
thf(2025,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(13186,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)],[2025]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( C @ ( B @ ( A @ k2_tarski ) @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_4) ).
thf(8199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( C @ ( B @ ( A @ k2_tarski ) @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1008,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(7881,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(2197,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(14199,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2197]) ).
thf(1740,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(11484,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)],[1740]) ).
thf(1754,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(11587,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)],[1754]) ).
thf(59,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(3022,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)],[59]) ).
thf(510,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(5455,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)],[510]) ).
thf(290,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(4252,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)],[290]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_membered )
& ( A @ v1_membered ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc42_membered) ).
thf(7161,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_membered )
& ( A @ v1_membered ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
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(7710,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(2381,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(14973,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)],[2381]) ).
thf(250,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(4091,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)],[250]) ).
thf(2418,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(15118,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)],[2418]) ).
thf(495,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(5366,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)],[495]) ).
thf(2412,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(15097,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)],[2412]) ).
thf(1536,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(10409,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)],[1536]) ).
thf(1111,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_boole) ).
thf(8334,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ k3_cqc_lang ) @ ( C @ k6_partfun1 @ k1_funct_4 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_7) ).
thf(7084,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ k3_cqc_lang ) @ ( C @ k6_partfun1 @ k1_funct_4 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(2276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ k2_tarski ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( C @ ( B @ k2_tarski ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_funct_4) ).
thf(14524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ k2_tarski ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( C @ ( B @ k2_tarski ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276]) ).
thf(1276,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(9126,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)],[1276]) ).
thf(372,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(4785,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)],[372]) ).
thf(2028,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(13218,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)],[2028]) ).
thf(2336,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k2_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_urysohn1) ).
thf(14772,plain,
k1_numbers @ k1_zfmisc_1 @ ( k2_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336]) ).
thf(1057,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(8081,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)],[1057]) ).
thf(75,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(3134,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)],[75]) ).
thf(379,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(4821,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)],[379]) ).
thf(500,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_relat_1) ).
thf(5396,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(679,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(6178,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)],[679]) ).
thf(1544,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(10441,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)],[1544]) ).
thf(1701,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(11212,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)],[1701]) ).
thf(742,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(6509,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)],[742]) ).
thf(1015,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(7906,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)],[1015]) ).
thf(265,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(4160,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)],[265]) ).
thf(176,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(3664,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)],[176]) ).
thf(1694,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(11191,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)],[1694]) ).
thf(1229,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(8878,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)],[1229]) ).
thf(150,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(3471,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)],[150]) ).
thf(904,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(7301,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)],[904]) ).
thf(1028,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(7957,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)],[1028]) ).
thf(1285,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(9177,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)],[1285]) ).
thf(1521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_enumset1) ).
thf(10330,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(244,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(4053,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)],[244]) ).
thf(532,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(5534,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)],[532]) ).
thf(2517,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(15638,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)],[2517]) ).
thf(863,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(7095,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)],[863]) ).
thf(108,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(3282,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)],[108]) ).
thf(1303,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(9264,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)],[1303]) ).
thf(864,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(7097,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)],[864]) ).
thf(1186,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(8683,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(2312,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(14680,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)],[2312]) ).
thf(2019,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(13158,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)],[2019]) ).
thf(589,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(5769,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)],[589]) ).
thf(1326,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(9380,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)],[1326]) ).
thf(223,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(3958,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)],[223]) ).
thf(294,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(4295,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)],[294]) ).
thf(1515,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(10263,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)],[1515]) ).
thf(2364,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(14889,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)],[2364]) ).
thf(86,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(3166,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)],[86]) ).
thf(2034,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(13254,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)],[2034]) ).
thf(1033,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).
thf(7977,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(2101,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(13654,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)],[2101]) ).
thf(622,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(5879,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)],[622]) ).
thf(571,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(5702,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)],[571]) ).
thf(558,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 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( G
= ( E @ ( B @ k12_finseq_1 ) ) )
=> ( ( G @ ( D @ ( F @ k5_funcop_1 ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ k12_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_finseq_2) ).
thf(5655,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 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( G
= ( E @ ( B @ k12_finseq_1 ) ) )
=> ( ( G @ ( D @ ( F @ k5_funcop_1 ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ k12_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1549,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k1_cat_1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k1_cat_1 ) ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cat_1) ).
thf(10502,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k1_cat_1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k1_cat_1 ) ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(1291,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(9217,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)],[1291]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( C @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mcart_1) ).
thf(4192,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( C @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(2403,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k2_finsub_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
thf(15050,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k2_finsub_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2403]) ).
thf(206,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(3810,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)],[206]) ).
thf(815,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(6848,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)],[815]) ).
thf(1142,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(8503,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)],[1142]) ).
thf(1073,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 @ k5_xboole_0 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k3_xboole_0 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_xboole_0 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_classes2) ).
thf(8145,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 @ k5_xboole_0 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k3_xboole_0 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_xboole_0 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(2219,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_0_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( 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_0_domain_1) ).
thf(14317,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] :
( ( 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_0_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i] :
( ( 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)],[2219]) ).
thf(724,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(6427,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)],[724]) ).
thf(651,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(6043,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)],[651]) ).
thf(44,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(2820,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)],[44]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(6445,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(413,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(4994,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)],[413]) ).
thf(1685,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 )
= ( A @ a_1_2_ens_1 @ k3_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_ens_1) ).
thf(11152,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 )
= ( A @ a_1_2_ens_1 @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(404,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(4947,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)],[404]) ).
thf(154,axiom,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_relat_1) ).
thf(3499,plain,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(2144,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(13924,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)],[2144]) ).
thf(164,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( A
= ( B @ k9_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_finseq_3) ).
thf(3578,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( A
= ( B @ k9_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(914,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(7361,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)],[914]) ).
thf(512,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(5460,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)],[512]) ).
thf(944,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(7503,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)],[944]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = F ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_mcart_1) ).
thf(6292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = F ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1567,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(10583,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)],[1567]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ k1_tarski @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_mcart_1) ).
thf(6972,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ k1_tarski @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1391,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(9626,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(1330,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(9391,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)],[1330]) ).
thf(1826,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_enumset1) ).
thf(12025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(997,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(7794,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)],[997]) ).
thf(1929,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(12618,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)],[1929]) ).
thf(2054,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(13359,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)],[2054]) ).
thf(1080,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(8181,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)],[1080]) ).
thf(538,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(5551,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)],[538]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ k9_finseq_1 @ v1_funct_1 )
& ( A @ k9_finseq_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_finseq_1) ).
thf(3144,plain,
! [A: $i] :
( ( A @ k9_finseq_1 @ v1_funct_1 )
& ( A @ k9_finseq_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(809,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(6833,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)],[809]) ).
thf(363,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(4746,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)],[363]) ).
thf(436,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(5113,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)],[436]) ).
thf(1337,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(9423,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1527,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(10367,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)],[1527]) ).
thf(943,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(7501,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)],[943]) ).
thf(1463,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = G ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_mcart_1) ).
thf(10006,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = G ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = G ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(716,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(6392,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)],[716]) ).
thf(2126,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(13835,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k1_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126]) ).
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(7713,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(2472,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(15368,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)],[2472]) ).
thf(1768,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(11670,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)],[1768]) ).
thf(2255,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(14452,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)],[2255]) ).
thf(361,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(4740,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(676,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(6168,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)],[676]) ).
thf(2284,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(14565,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284]) ).
thf(1716,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(11284,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)],[1716]) ).
thf(254,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(4104,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)],[254]) ).
thf(1574,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(10615,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)],[1574]) ).
thf(2108,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(13681,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)],[2108]) ).
thf(578,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ k2_mcart_1 @ ( B @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ k4_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_ens_1) ).
thf(5729,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ k2_mcart_1 @ ( B @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ k4_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1388,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(9613,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)],[1388]) ).
thf(1104,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(8287,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)],[1104]) ).
thf(1774,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(11702,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)],[1774]) ).
thf(321,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(4461,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)],[321]) ).
thf(177,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(3667,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)],[177]) ).
thf(1909,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_enumset1) ).
thf(12478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).
thf(2178,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(14100,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)],[2178]) ).
thf(1560,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(10543,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)],[1560]) ).
thf(1070,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(8136,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)],[1070]) ).
thf(61,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(3033,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)],[61]) ).
thf(2018,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(13153,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)],[2018]) ).
thf(1566,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(10580,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(526,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(5515,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)],[526]) ).
thf(247,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ v2_funct_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_functor1) ).
thf(4063,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ v2_funct_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1268,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(9095,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)],[1268]) ).
thf(783,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(6728,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)],[783]) ).
thf(1824,axiom,
~ ( k2_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_qc_lang1) ).
thf(12016,plain,
~ ( k2_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824]) ).
thf(243,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(4048,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)],[243]) ).
thf(1231,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(8884,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)],[1231]) ).
thf(1364,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(9525,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)],[1364]) ).
thf(1999,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(13074,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)],[1999]) ).
thf(292,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(4263,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)],[292]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(7750,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1133,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(8462,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)],[1133]) ).
thf(614,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(5854,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)],[614]) ).
thf(911,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(7346,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)],[911]) ).
thf(1879,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(12353,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)],[1879]) ).
thf(1146,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(8530,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(790,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(6748,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)],[790]) ).
thf(897,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(7281,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1729,axiom,
( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( k7_vectsp_2 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( k7_vectsp_2 @ v1_funct_2 ) ) )
& ( k7_vectsp_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_vectsp_2) ).
thf(11356,plain,
( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( k7_vectsp_2 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( k7_vectsp_2 @ v1_funct_2 ) ) )
& ( k7_vectsp_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(168,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(3615,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)],[168]) ).
thf(722,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(6413,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)],[722]) ).
thf(1972,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(12863,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)],[1972]) ).
thf(2569,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(15826,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)],[2569]) ).
thf(1955,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(12769,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).
thf(2008,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(13116,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)],[2008]) ).
thf(573,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(5714,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(2448,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(15243,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)],[2448]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ k2_tarski ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( ( A @ k2_mcart_1 )
= E )
| ( ( A @ k2_mcart_1 )
= D ) )
& ( ( ( A @ k1_mcart_1 )
= C )
| ( ( A @ k1_mcart_1 )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_mcart_1) ).
thf(3831,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ k2_tarski ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( ( A @ k2_mcart_1 )
= E )
| ( ( A @ k2_mcart_1 )
= D ) )
& ( ( ( A @ k1_mcart_1 )
= C )
| ( ( A @ k1_mcart_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1865,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(12264,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)],[1865]) ).
thf(458,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(5221,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)],[458]) ).
thf(1150,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(8545,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)],[1150]) ).
thf(103,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(3254,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)],[103]) ).
thf(1603,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(10748,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)],[1603]) ).
thf(134,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(3413,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)],[134]) ).
thf(1891,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(12404,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)],[1891]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finseq_1) ).
thf(2990,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(2539,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(15714,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)],[2539]) ).
thf(803,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(6801,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)],[803]) ).
thf(471,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(5270,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( E @ k1_funct_1 ) @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( C @ ( E @ m1_pboole ) )
& ( B @ ( D @ m1_pboole ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_functor0 ) ) ) ) ) @ ( A @ r2_hidden ) )
<=> ? [H: $i] :
( ( A
= ( G @ ( H @ ( D @ k1_funct_1 ) @ k10_pboole ) @ ( H @ k4_tarski ) ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_functor0) ).
thf(7962,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( E @ k1_funct_1 ) @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( C @ ( E @ m1_pboole ) )
& ( B @ ( D @ m1_pboole ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [H: $i] :
( ( A
= ( G @ ( H @ ( D @ k1_funct_1 ) @ k10_pboole ) @ ( H @ k4_tarski ) ) )
& ( B @ ( H @ m1_subset_1 ) ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_functor0 ) ) ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_functor0 ) ) ) ) ) @ ( A @ r2_hidden ) )
=> ? [H: $i] :
( ( A
= ( G @ ( H @ ( D @ k1_funct_1 ) @ k10_pboole ) @ ( H @ k4_tarski ) ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(563,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(5673,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)],[563]) ).
thf(507,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(5423,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)],[507]) ).
thf(2575,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_classes2 ) )
= ( B @ k1_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_classes2) ).
thf(15847,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_classes2 ) )
= ( B @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2575]) ).
thf(2161,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(14028,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)],[2161]) ).
thf(216,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(3862,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)],[216]) ).
thf(1039,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(8009,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)],[1039]) ).
thf(492,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(5345,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)],[492]) ).
thf(1889,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(12382,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)],[1889]) ).
thf(647,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(6028,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)],[647]) ).
thf(1103,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(8282,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)],[1103]) ).
thf(2073,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(13487,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)],[2073]) ).
thf(1782,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(11762,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)],[1782]) ).
thf(2215,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(14302,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)],[2215]) ).
thf(734,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(6459,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)],[734]) ).
thf(1409,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(9773,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)],[1409]) ).
thf(2227,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(14353,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)],[2227]) ).
thf(1166,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(8604,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)],[1166]) ).
thf(919,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(7389,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_card_fil ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(347,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 @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_4) ).
thf(4636,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 @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1054,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(8063,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)],[1054]) ).
thf(1582,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(10644,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)],[1582]) ).
thf(1126,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(8435,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)],[1126]) ).
thf(686,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(6235,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)],[686]) ).
thf(386,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(4845,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)],[386]) ).
thf(1169,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(8619,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(2310,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(14666,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)],[2310]) ).
thf(1660,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(11057,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)],[1660]) ).
thf(1041,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(8014,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)],[1041]) ).
thf(2137,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(13872,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)],[2137]) ).
thf(2234,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(14381,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)],[2234]) ).
thf(283,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(4227,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)],[283]) ).
thf(2436,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(15189,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)],[2436]) ).
thf(2007,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(13099,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)],[2007]) ).
thf(1533,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(10398,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)],[1533]) ).
thf(384,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(4840,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)],[384]) ).
thf(1466,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(10021,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)],[1466]) ).
thf(391,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(4883,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)],[391]) ).
thf(1608,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(10771,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)],[1608]) ).
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(12667,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(2438,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( B
= ( A @ ( B @ k1_toler_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_yellow_0) ).
thf(15201,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( B
= ( A @ ( B @ k1_toler_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2438]) ).
thf(99,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k10_finseq_1 ) @ k5_relat_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( B @ ( A @ k1_funct_1 ) @ k10_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_finseq_2) ).
thf(3237,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k10_finseq_1 ) @ k5_relat_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( B @ ( A @ k1_funct_1 ) @ k10_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1181,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(8662,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)],[1181]) ).
thf(1631,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(10880,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)],[1631]) ).
thf(2510,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(15599,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)],[2510]) ).
thf(935,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_fraenkel) ).
thf(7468,plain,
! [A: $i,B: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(2002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_enumset1) ).
thf(13084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(282,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(4219,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)],[282]) ).
thf(1829,axiom,
f2_s17_fraenkel @ ( a_0_32_fraenkel @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s17_fraenkel) ).
thf(12033,plain,
f2_s17_fraenkel @ ( a_0_32_fraenkel @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).
thf(1991,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_finseq_2 ) ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_finseq_2) ).
thf(12974,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_finseq_2 ) ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991]) ).
thf(2068,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(13434,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)],[2068]) ).
thf(2431,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_subset_1 ) )
=> ( A @ ( B @ r2_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_subset_1) ).
thf(15168,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_subset_1 ) )
=> ( A @ ( B @ r2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2431]) ).
thf(355,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(4721,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)],[355]) ).
thf(1339,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(9429,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)],[1339]) ).
thf(1063,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(8100,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)],[1063]) ).
thf(1670,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(11088,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)],[1670]) ).
thf(1376,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(9566,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)],[1376]) ).
thf(1078,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(8176,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)],[1078]) ).
thf(2061,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(13394,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)],[2061]) ).
thf(928,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(7435,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)],[928]) ).
thf(114,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(3311,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)],[114]) ).
thf(2250,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_classes2 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_classes2) ).
thf(14437,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_classes2 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250]) ).
thf(335,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(4518,plain,
! [A: $i] : ( A @ k9_setwiseo @ ( A @ k1_setwiseo @ ( A @ k5_finsub_1 @ r3_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1191,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(8704,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)],[1191]) ).
thf(1786,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m4_realset1 ) )
<=> ? [C: $i] :
( ( B
= ( C @ k1_tarski ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_realset1) ).
thf(11782,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( ? [C: $i] :
( ( B
= ( C @ k1_tarski ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ m4_realset1 ) ) )
& ( ( A @ ( B @ m4_realset1 ) )
=> ? [C: $i] :
( ( B
= ( C @ k1_tarski ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(2356,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(14860,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)],[2356]) ).
thf(295,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(4301,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)],[295]) ).
thf(1848,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k4_partfun1 ) @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_partfun1) ).
thf(12151,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k4_partfun1 ) @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).
thf(2405,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(15054,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)],[2405]) ).
thf(2297,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(14613,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)],[2297]) ).
thf(1593,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 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_2) ).
thf(10708,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 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(2501,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k10_classes2 ) ) )
= ( B @ ( C @ ( A @ k10_classes2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k10_classes2) ).
thf(15545,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k10_classes2 ) ) )
= ( B @ ( C @ ( A @ k10_classes2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k4_xboole_0 ) ) )
& ( ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k3_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_sysrel) ).
thf(8105,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k4_xboole_0 ) ) )
& ( ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k3_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(835,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(6967,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)],[835]) ).
thf(1619,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k1_finsub_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_finsub_1) ).
thf(10830,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k1_finsub_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(603,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(5818,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)],[603]) ).
thf(1859,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(12223,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)],[1859]) ).
thf(2277,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(14529,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)],[2277]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = I ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_mcart_1) ).
thf(7631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = I ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = I ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1332,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(9397,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)],[1332]) ).
thf(1246,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(8985,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)],[1246]) ).
thf(2500,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(15523,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)],[2500]) ).
thf(2289,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( A @ k2_ens_1 @ ( A @ k9_ens_1 @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( A @ k9_ens_1 @ v1_funct_2 ) ) )
& ( A @ k9_ens_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_ens_1) ).
thf(14580,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( A @ k2_ens_1 @ ( A @ k9_ens_1 @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( A @ k9_ens_1 @ v1_funct_2 ) ) )
& ( A @ k9_ens_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289]) ).
thf(2044,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(13291,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)],[2044]) ).
thf(1396,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(9662,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)],[1396]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(7717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1758,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(11625,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)],[1758]) ).
thf(435,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(5107,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)],[435]) ).
thf(2429,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(15162,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)],[2429]) ).
thf(1960,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(12818,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)],[1960]) ).
thf(711,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(6363,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)],[711]) ).
thf(1530,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(10381,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)],[1530]) ).
thf(1403,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(9714,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)],[1403]) ).
thf(1338,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(9426,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)],[1338]) ).
thf(2026,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(13190,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)],[2026]) ).
thf(2402,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_classes2 ) ) )
= ( B @ ( C @ ( A @ k5_classes2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_classes2) ).
thf(15047,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_classes2 ) ) )
= ( B @ ( C @ ( A @ k5_classes2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402]) ).
thf(697,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(6304,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)],[697]) ).
thf(298,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(4315,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)],[298]) ).
thf(2393,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(15022,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)],[2393]) ).
thf(1610,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ v1_zf_model )
=> ( k2_zfrefle1 @ ( A @ r1_zfrefle1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_zfrefle1) ).
thf(10776,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ v1_zf_model )
=> ( k2_zfrefle1 @ ( A @ r1_zfrefle1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(365,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(4750,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)],[365]) ).
thf(466,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(5253,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)],[466]) ).
thf(595,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(5786,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)],[595]) ).
thf(1164,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(8594,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)],[1164]) ).
thf(1387,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(9609,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)],[1387]) ).
thf(1615,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( ( A @ ( B @ v2_card_fil ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_card_fil) ).
thf(10798,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ v2_card_fil ) ) )
& ( ( A @ ( B @ v2_card_fil ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(1708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k11_classes2 ) ) )
= ( C @ ( B @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_classes2) ).
thf(11243,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k11_classes2 ) ) )
= ( C @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(311,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(4406,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)],[311]) ).
thf(2562,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(15803,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)],[2562]) ).
thf(2516,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( A @ k2_classes2 ) @ m1_subset_1 ) )
& ~ ( B @ ( A @ k2_classes2 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_classes2) ).
thf(15634,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( A @ k2_classes2 ) @ m1_subset_1 ) )
& ~ ( B @ ( A @ k2_classes2 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2516]) ).
thf(333,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(4513,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)],[333]) ).
thf(2193,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(14189,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)],[2193]) ).
thf(1100,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(8275,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)],[1100]) ).
thf(765,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(6630,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)],[765]) ).
thf(795,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(6763,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)],[795]) ).
thf(1270,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(9100,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)],[1270]) ).
thf(139,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(3428,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)],[139]) ).
thf(2454,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(15270,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)],[2454]) ).
thf(560,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(5662,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)],[560]) ).
thf(839,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(6978,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)],[839]) ).
thf(1784,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(11774,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)],[1784]) ).
thf(1901,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(12454,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)],[1901]) ).
thf(1672,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(11097,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(1559,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(10539,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)],[1559]) ).
thf(2543,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(15728,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)],[2543]) ).
thf(2024,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(13184,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)],[2024]) ).
thf(2455,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(15275,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)],[2455]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(6539,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1120,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(8390,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)],[1120]) ).
thf(763,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(6625,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)],[763]) ).
thf(320,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(4457,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)],[320]) ).
thf(961,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(7572,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)],[961]) ).
thf(1605,axiom,
~ ( k1_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_qc_lang1) ).
thf(10752,plain,
~ ( k1_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(831,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(6935,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)],[831]) ).
thf(11,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(2649,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)],[11]) ).
thf(2496,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(15510,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)],[2496]) ).
thf(656,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(6065,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)],[656]) ).
thf(2001,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_enumset1) ).
thf(13081,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001]) ).
thf(1252,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(9012,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)],[1252]) ).
thf(1804,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(11888,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)],[1804]) ).
thf(1554,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(10518,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1279,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(9144,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)],[1279]) ).
thf(483,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(5317,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)],[483]) ).
thf(1655,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(11023,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)],[1655]) ).
thf(1677,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(11129,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)],[1677]) ).
thf(671,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 @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( B
= ( A @ k1_tarski @ ( C @ k2_xboole_0 ) ) ) )
=> ( ( B @ ( A @ k2_cantor_1 ) )
= ( C @ ( A @ k2_cantor_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_yellow_9) ).
thf(6134,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 @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( B
= ( A @ k1_tarski @ ( C @ k2_xboole_0 ) ) ) )
=> ( ( B @ ( A @ k2_cantor_1 ) )
= ( C @ ( A @ k2_cantor_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(2507,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(15584,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)],[2507]) ).
thf(1893,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(12418,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)],[1893]) ).
thf(151,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(3486,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)],[151]) ).
thf(2506,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(15582,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)],[2506]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_finseq_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_finset_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_finseq_1) ).
thf(3654,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_finseq_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_finset_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k9_funct_2 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k3_cqc_lang ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_altcat_1) ).
thf(8219,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k9_funct_2 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k3_cqc_lang ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(958,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(7544,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)],[958]) ).
thf(2522,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(15664,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)],[2522]) ).
thf(577,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(5726,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)],[577]) ).
thf(2341,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(14784,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)],[2341]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k9_finseq_1 )
!= ( C @ ( B @ k10_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_finseq_3) ).
thf(4384,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k9_finseq_1 )
!= ( C @ ( B @ k10_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1910,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(12481,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)],[1910]) ).
thf(2343,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(14799,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)],[2343]) ).
thf(933,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(7463,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)],[933]) ).
thf(47,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 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_4) ).
thf(2836,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 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_4 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_4 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(2592,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k15_ens_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_ens_1) ).
thf(15972,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k15_ens_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2592]) ).
thf(1857,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(12218,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)],[1857]) ).
thf(2021,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(13169,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)],[2021]) ).
thf(2585,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(15927,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)],[2585]) ).
thf(2305,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(14655,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)],[2305]) ).
thf(1897,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(12429,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)],[1897]) ).
thf(1612,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(10787,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)],[1612]) ).
thf(1313,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(9316,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)],[1313]) ).
thf(2090,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_partfun1 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_partfun1) ).
thf(13607,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_partfun1 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090]) ).
thf(407,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(4970,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1923,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(12532,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)],[1923]) ).
thf(1357,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(9498,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(800,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(6788,plain,
! [A: $i] :
( ( A @ k9_setwiseo @ ( A @ k5_finsub_1 @ k3_binop_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1046,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(8036,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)],[1046]) ).
thf(1443,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(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] :
( ( 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)],[1443]) ).
thf(2128,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(13839,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)],[2128]) ).
thf(1974,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(12870,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)],[1974]) ).
thf(522,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(5498,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)],[522]) ).
thf(1739,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(11474,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)],[1739]) ).
thf(1380,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(9581,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)],[1380]) ).
thf(2311,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(14670,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)],[2311]) ).
thf(1448,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
= ( k1_xboole_0 @ k1_tarski @ ( C @ k2_xboole_0 ) ) )
| ( C
= ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ) )
=> ( ( B @ ( A @ k1_cantor_1 ) )
= ( C @ ( A @ k1_cantor_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_waybel18) ).
thf(9932,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
= ( k1_xboole_0 @ k1_tarski @ ( C @ k2_xboole_0 ) ) )
| ( C
= ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ) )
=> ( ( B @ ( A @ k1_cantor_1 ) )
= ( C @ ( A @ k1_cantor_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(129,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(3390,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)],[129]) ).
thf(2135,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(13868,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)],[2135]) ).
thf(1494,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(10148,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)],[1494]) ).
thf(339,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(4540,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)],[339]) ).
thf(1201,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_numbers) ).
thf(8732,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(852,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 @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_partfun1) ).
thf(7027,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(567,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_realset1 ) ) )
= ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_realset1) ).
thf(5683,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_realset1 ) ) )
= ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1543,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(10438,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)],[1543]) ).
thf(1727,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(11347,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)],[1727]) ).
thf(2445,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(15232,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)],[2445]) ).
thf(964,axiom,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(7614,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1984,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(12946,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)],[1984]) ).
thf(892,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(7261,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)],[892]) ).
thf(2020,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(13167,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).
thf(1208,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(8775,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(102,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(3247,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)],[102]) ).
thf(49,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(2862,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)],[49]) ).
thf(36,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 @ k2_xboole_0 ) )
!= C ) )
& ! [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',t2_partfun1) ).
thf(2766,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 @ k2_xboole_0 ) )
!= C ) )
& ! [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)],[36]) ).
thf(2328,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(14757,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)],[2328]) ).
thf(2273,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(14516,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)],[2273]) ).
thf(2300,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(14634,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)],[2300]) ).
thf(1872,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_enumset1) ).
thf(12310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).
thf(2183,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(14125,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)],[2183]) ).
thf(1386,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(9607,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)],[1386]) ).
thf(118,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(3333,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)],[118]) ).
thf(2085,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(13591,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085]) ).
thf(1504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( A @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_enumset1) ).
thf(10180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( A @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(291,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(4259,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)],[291]) ).
thf(1072,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(8142,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)],[1072]) ).
thf(1479,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(10075,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)],[1479]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k12_finseq_1 ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_finseq_1) ).
thf(3005,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k12_finseq_1 ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(2051,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(13340,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)],[2051]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(7624,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1811,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_toler_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_triang_1) ).
thf(11927,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_toler_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(1671,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 ) )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( C @ ( A @ r2_hidden ) )
& ( C = D ) )
=> ( ( D @ ( B @ k2_cantor_1 ) )
= ( C @ ( A @ k2_cantor_1 ) @ ( B @ k1_tarski @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_yellow_9) ).
thf(11093,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 ) )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( C @ ( A @ r2_hidden ) )
& ( C = D ) )
=> ( ( D @ ( B @ k2_cantor_1 ) )
= ( C @ ( A @ k2_cantor_1 ) @ ( B @ k1_tarski @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(1714,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(11274,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)],[1714]) ).
thf(682,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(6224,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)],[682]) ).
thf(1964,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(12831,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)],[1964]) ).
thf(876,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(7174,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)],[876]) ).
thf(91,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(3201,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)],[91]) ).
thf(1323,axiom,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(9372,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(94,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(3215,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)],[94]) ).
thf(1813,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(11933,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)],[1813]) ).
thf(1988,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(12962,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)],[1988]) ).
thf(517,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(5479,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)],[517]) ).
thf(2419,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(15121,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419]) ).
thf(747,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(6533,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)],[747]) ).
thf(1305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ k1_tarski @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_enumset1) ).
thf(9269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ k1_tarski @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(759,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(6592,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)],[759]) ).
thf(1282,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(9169,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)],[1282]) ).
thf(397,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(4906,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)],[397]) ).
thf(2139,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(13879,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)],[2139]) ).
thf(1880,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(12361,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).
thf(1458,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(9985,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)],[1458]) ).
thf(447,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m4_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_realset1) ).
thf(5170,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m4_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(266,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(4163,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)],[266]) ).
thf(2246,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(14424,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)],[2246]) ).
thf(1551,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(10510,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)],[1551]) ).
thf(1583,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(10651,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)],[1583]) ).
thf(1367,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(9534,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)],[1367]) ).
thf(264,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(4148,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)],[264]) ).
thf(31,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(2749,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)],[31]) ).
thf(721,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(6409,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)],[721]) ).
thf(870,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(7150,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)],[870]) ).
thf(539,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(5557,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)],[539]) ).
thf(2306,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(14657,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)],[2306]) ).
thf(2320,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(14713,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)],[2320]) ).
thf(2399,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(15039,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)],[2399]) ).
thf(1952,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(12751,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)],[1952]) ).
thf(1349,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(9468,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)],[1349]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( D
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_mcart_1) ).
thf(8839,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( D
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(2400,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k1_classes2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_classes2) ).
thf(15042,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k1_classes2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400]) ).
thf(349,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(4644,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)],[349]) ).
thf(834,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(6963,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)],[834]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( A @ k3_ens_1 ) )
= ( B @ ( A @ k4_ens_1 ) ) )
& ( ( B @ ( A @ k3_ens_1 ) )
= ( C @ ( A @ k4_ens_1 ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k6_ens_1 ) ) @ ( A @ k6_ens_1 ) ) )
= ( D @ ( B @ ( A @ k6_ens_1 ) ) @ ( C @ ( A @ k6_ens_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ens_1) ).
thf(3225,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( A @ k3_ens_1 ) )
= ( B @ ( A @ k4_ens_1 ) ) )
& ( ( B @ ( A @ k3_ens_1 ) )
= ( C @ ( A @ k4_ens_1 ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k6_ens_1 ) ) @ ( A @ k6_ens_1 ) ) )
= ( D @ ( B @ ( A @ k6_ens_1 ) ) @ ( C @ ( A @ k6_ens_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1870,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_finseq_2) ).
thf(12305,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = H ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_mcart_1) ).
thf(5402,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = H ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = H ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ? [D: $i] :
( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_mcart_1) ).
thf(7407,plain,
! [A: $i,B: $i,C: $i] :
~ ( ? [D: $i] :
( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(1086,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(8205,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)],[1086]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_enumset1) ).
thf(8482,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(2064,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(13404,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)],[2064]) ).
thf(371,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(4782,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)],[371]) ).
thf(1454,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(9964,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)],[1454]) ).
thf(107,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(3279,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)],[107]) ).
thf(392,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(4889,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)],[392]) ).
thf(2157,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(14008,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)],[2157]) ).
thf(368,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(4765,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)],[368]) ).
thf(1600,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(10740,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)],[1600]) ).
thf(1906,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(12469,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)],[1906]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_ens_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k1_funct_2 ) ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_ens_1) ).
thf(7397,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k1_funct_2 ) ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_ens_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_ens_1 @ ( A @ r2_hidden ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k1_funct_2 ) ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(608,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k3_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k5_xboole_0 ) @ r2_hidden ) ) ) ) )
=> ( A @ v4_finsub_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finsub_1) ).
thf(5833,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k3_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k5_xboole_0 ) @ r2_hidden ) ) ) ) )
=> ( A @ v4_finsub_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(780,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(6716,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)],[780]) ).
thf(504,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(5415,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)],[504]) ).
thf(1154,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(8559,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)],[1154]) ).
thf(1477,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ k2_enumset1 ) ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_enumset1) ).
thf(10069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ k2_enumset1 ) ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(2162,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(14035,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)],[2162]) ).
thf(1121,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_relat_1) ).
thf(8393,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(2123,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_realset1) ).
thf(13772,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123]) ).
thf(658,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_cqc_lang ) @ v1_funct_1 )
& ( B @ ( A @ k3_cqc_lang ) @ v1_relat_1 )
& ~ ( B @ ( A @ k3_cqc_lang ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_7) ).
thf(6070,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_cqc_lang ) @ v1_funct_1 )
& ( B @ ( A @ k3_cqc_lang ) @ v1_relat_1 )
& ~ ( B @ ( A @ k3_cqc_lang ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(116,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(3321,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)],[116]) ).
thf(1912,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(12486,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912]) ).
thf(1580,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(10635,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)],[1580]) ).
thf(1407,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(9750,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)],[1407]) ).
thf(1662,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(11065,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)],[1662]) ).
thf(1308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = G ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_mcart_1) ).
thf(9284,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = G ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(2016,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( k7_vectsp_2 @ r2_hidden ) )
& ( A @ ( k2_midsp_1 @ r2_hidden ) )
& ( A @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ r2_hidden ) )
& ( A @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_grcat_1) ).
thf(13137,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( k7_vectsp_2 @ r2_hidden ) )
& ( A @ ( k2_midsp_1 @ r2_hidden ) )
& ( A @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ r2_hidden ) )
& ( A @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).
thf(2581,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ p1_s5_domain_1 )
=> ( B @ p2_s5_domain_1 ) ) )
=> ( A @ a_1_4_domain_1 @ ( A @ a_1_3_domain_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s5_domain_1) ).
thf(15908,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ p1_s5_domain_1 )
=> ( B @ p2_s5_domain_1 ) ) )
=> ( A @ a_1_4_domain_1 @ ( A @ a_1_3_domain_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581]) ).
thf(840,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(6982,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)],[840]) ).
thf(2466,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(15344,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)],[2466]) ).
thf(900,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(7289,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)],[900]) ).
thf(1405,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(9744,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(700,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(6311,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)],[700]) ).
thf(1031,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(7972,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(5249,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(816,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(6869,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)],[816]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_subset_1 ) )
<=> ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_subset_1) ).
thf(7106,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( A @ r2_subset_1 ) ) )
& ( ( B @ ( A @ r2_subset_1 ) )
=> ( B @ ( A @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(5872,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(180,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(3675,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)],[180]) ).
thf(1293,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(9226,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)],[1293]) ).
thf(2287,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(14573,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_7 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287]) ).
thf(1649,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(10983,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)],[1649]) ).
thf(2386,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(14997,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)],[2386]) ).
thf(1300,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(9256,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
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(12677,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(205,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(3807,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)],[205]) ).
thf(2206,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(14231,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)],[2206]) ).
thf(2160,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(14020,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)],[2160]) ).
thf(661,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(6084,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)],[661]) ).
thf(423,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(5048,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)],[423]) ).
thf(1225,axiom,
! [A: $i] :
( ( A @ v4_finsub_1 )
<=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(8859,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ) )
=> ( A @ v4_finsub_1 ) )
& ( ( A @ v4_finsub_1 )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(5758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1634,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(10890,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)],[1634]) ).
thf(83,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(3158,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)],[83]) ).
thf(1849,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(12155,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)],[1849]) ).
thf(2179,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_2) ).
thf(14107,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179]) ).
thf(401,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(4921,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)],[401]) ).
thf(1752,axiom,
! [A: $i,B: $i] :
( ( ( k2_qc_lang1 @ ( B @ m1_subset_1 ) )
& ( k4_qc_lang1 @ ( A @ m1_subset_1 ) ) )
=> ( ( k1_qc_lang1 @ ( k4_qc_lang1 @ ( B @ ( A @ k6_cqc_lang ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k6_cqc_lang ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_cqc_lang) ).
thf(11578,plain,
! [A: $i,B: $i] :
( ( ( k2_qc_lang1 @ ( B @ m1_subset_1 ) )
& ( k4_qc_lang1 @ ( A @ m1_subset_1 ) ) )
=> ( ( k1_qc_lang1 @ ( k4_qc_lang1 @ ( B @ ( A @ k6_cqc_lang ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k6_cqc_lang ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(23,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(2729,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)],[23]) ).
thf(1272,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(9107,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(1352,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( G @ m2_finseq_2 ) ) )
=> ( D @ ( A @ k4_finseq_2 ) @ ( D @ ( G @ ( E @ ( F @ k5_funcop_1 ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_finseq_2) ).
thf(9484,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( G @ m2_finseq_2 ) ) )
=> ( D @ ( A @ k4_finseq_2 ) @ ( D @ ( G @ ( E @ ( F @ k5_funcop_1 ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
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(12238,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(1623,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(10840,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)],[1623]) ).
thf(2407,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(15062,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)],[2407]) ).
thf(1772,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(11692,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)],[1772]) ).
thf(1970,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(12857,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)],[1970]) ).
thf(1850,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(12168,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)],[1850]) ).
thf(1573,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(10607,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)],[1573]) ).
thf(1502,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(10175,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)],[1502]) ).
thf(2331,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(14762,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)],[2331]) ).
thf(2268,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(14497,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)],[2268]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_mcart_1) ).
thf(6026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1646,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ( ~ ( A @ v2_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow21) ).
thf(10971,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ( ~ ( A @ v2_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(1762,axiom,
( ( k4_urysohn1 @ v2_membered )
& ( k4_urysohn1 @ v1_membered )
& ~ ( k4_urysohn1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_urysohn1) ).
thf(11638,plain,
( ( k4_urysohn1 @ v2_membered )
& ( k4_urysohn1 @ v1_membered )
& ~ ( k4_urysohn1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(257,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(4116,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)],[257]) ).
thf(124,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ k7_relat_1 ) @ ( B @ ( A @ k7_relat_1 ) @ k1_funct_4 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_4) ).
thf(3358,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ k7_relat_1 ) @ ( B @ ( A @ k7_relat_1 ) @ k1_funct_4 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(762,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(6615,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)],[762]) ).
thf(586,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(5762,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)],[586]) ).
thf(1680,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(11138,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)],[1680]) ).
thf(64,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(3042,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)],[64]) ).
thf(2503,axiom,
! [A: $i] :
( ( ( A @ v2_cat_5 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_cat_5 ) )
<=> ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_cat_5) ).
thf(15570,plain,
! [A: $i] :
( ( ( A @ v2_cat_5 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ m1_cat_5 ) ) )
& ( ( A @ ( B @ m1_cat_5 ) )
=> ( A @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503]) ).
thf(2526,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k11_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_classes2) ).
thf(15675,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k11_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2526]) ).
thf(1508,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(10202,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)],[1508]) ).
thf(1959,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(12813,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)],[1959]) ).
thf(776,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(6699,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)],[776]) ).
thf(1424,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(9821,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)],[1424]) ).
thf(1401,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_partfun1 ) @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_funct_2) ).
thf(9709,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_partfun1 ) @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(1194,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(8713,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)],[1194]) ).
thf(846,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(7010,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)],[846]) ).
thf(152,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(3491,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)],[152]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( B @ ( B @ ( A @ k1_toler_1 ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_toler_1) ).
thf(7742,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( B @ ( B @ ( A @ k1_toler_1 ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(978,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(7706,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)],[978]) ).
thf(2291,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(14593,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)],[2291]) ).
thf(1966,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(12842,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966]) ).
thf(1200,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(8728,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)],[1200]) ).
thf(990,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(7753,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)],[990]) ).
thf(2324,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(14744,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)],[2324]) ).
thf(1383,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(9594,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)],[1383]) ).
thf(2133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_enumset1) ).
thf(13864,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133]) ).
thf(550,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(5608,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)],[550]) ).
thf(376,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(4797,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)],[376]) ).
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(2602,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(1334,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(9404,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)],[1334]) ).
thf(732,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(6454,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)],[732]) ).
thf(25,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(2734,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)],[25]) ).
thf(431,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(5095,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)],[431]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_pboole ) )
= ( B @ ( A @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_pboole) ).
thf(6228,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_pboole ) )
= ( B @ ( A @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(2463,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k10_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_classes2) ).
thf(15334,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k10_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463]) ).
thf(995,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(7785,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)],[995]) ).
thf(183,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(3686,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)],[183]) ).
thf(1576,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(10625,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)],[1576]) ).
thf(326,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(4489,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)],[326]) ).
thf(1228,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(8874,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(2046,axiom,
( ( f2_s21_fraenkel @ v1_finset_1 )
=> ( a_0_38_fraenkel @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s21_fraenkel) ).
thf(13296,plain,
( ( f2_s21_fraenkel @ v1_finset_1 )
=> ( a_0_38_fraenkel @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).
thf(2170,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(14072,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)],[2170]) ).
thf(1962,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(12827,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)],[1962]) ).
thf(963,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_enumset1) ).
thf(7611,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(351,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(4662,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)],[351]) ).
thf(1507,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(10194,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)],[1507]) ).
thf(1761,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(11633,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)],[1761]) ).
thf(2033,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(13249,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)],[2033]) ).
thf(2370,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(14915,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)],[2370]) ).
thf(830,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_ens_1 ) @ ( A @ k4_ens_1 ) )
= B )
& ( ( B @ ( A @ k5_ens_1 ) @ ( A @ k3_ens_1 ) )
= B )
& ( ( B @ ( A @ k5_ens_1 ) @ k2_mcart_1 )
= ( B @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_ens_1) ).
thf(6927,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_ens_1 ) @ ( A @ k4_ens_1 ) )
= B )
& ( ( B @ ( A @ k5_ens_1 ) @ ( A @ k3_ens_1 ) )
= B )
& ( ( B @ ( A @ k5_ens_1 ) @ k2_mcart_1 )
= ( B @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(377,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(4801,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)],[377]) ).
thf(1227,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(8872,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)],[1227]) ).
thf(575,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(5720,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)],[575]) ).
thf(1827,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(12028,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)],[1827]) ).
thf(2482,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(15423,plain,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k3_qc_lang1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2482]) ).
thf(2434,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(15180,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)],[2434]) ).
thf(2152,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(13973,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)],[2152]) ).
thf(2470,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(15363,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)],[2470]) ).
thf(90,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(3187,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)],[90]) ).
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(9010,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(1263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = H ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_mcart_1) ).
thf(9062,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = H ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(2259,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(14466,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)],[2259]) ).
thf(2330,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(14760,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)],[2330]) ).
thf(2567,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(15821,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2567]) ).
thf(1205,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(8762,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)],[1205]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( E @ ( D @ k9_funct_2 ) ) )
= ( E @ k1_tarski @ ( D @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_7) ).
thf(3504,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( E @ ( D @ k9_funct_2 ) ) )
= ( E @ k1_tarski @ ( D @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(328,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(4494,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)],[328]) ).
thf(1796,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(11836,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)],[1796]) ).
thf(520,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(5488,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)],[520]) ).
thf(2249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ k2_enumset1 ) ) ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_enumset1) ).
thf(14434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ k2_enumset1 ) ) ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249]) ).
thf(664,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(6108,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)],[664]) ).
thf(2385,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(14994,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)],[2385]) ).
thf(100,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 @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_partfun1) ).
thf(3240,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 @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(832,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(6949,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)],[832]) ).
thf(38,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(2789,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)],[38]) ).
thf(426,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(5065,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)],[426]) ).
thf(611,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(5844,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)],[611]) ).
thf(12,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(2657,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)],[12]) ).
thf(2264,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_partfun1) ).
thf(14481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264]) ).
thf(939,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(7487,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)],[939]) ).
thf(1071,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(8139,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)],[1071]) ).
thf(2081,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(13550,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)],[2081]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(7223,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1789,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(11804,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)],[1789]) ).
thf(1092,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(8222,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)],[1092]) ).
thf(1366,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(9531,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)],[1366]) ).
thf(1800,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(11861,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)],[1800]) ).
thf(607,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
thf(5831,plain,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1853,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(12184,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)],[1853]) ).
thf(1957,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(12776,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)],[1957]) ).
thf(2011,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(13125,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)],[2011]) ).
thf(2041,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k1_enumset1 ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_enumset1) ).
thf(13281,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ k1_enumset1 ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).
thf(1777,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B
= ( A @ k15_classes2 ) )
<=> ( ! [C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_classes2) ).
thf(11729,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( ! [C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( A @ k15_classes2 ) ) )
& ( ( B
= ( A @ k15_classes2 ) )
=> ( ! [C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(977,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(7704,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(621,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_domain_1) ).
thf(5876,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(41,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(2806,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)],[41]) ).
thf(2055,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(13363,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)],[2055]) ).
thf(432,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(5097,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)],[432]) ).
thf(1160,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(8581,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)],[1160]) ).
thf(1547,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(10461,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)],[1547]) ).
thf(2411,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(15079,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)],[2411]) ).
thf(1542,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(10435,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)],[1542]) ).
thf(878,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(7180,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)],[878]) ).
thf(1061,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(8092,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)],[1061]) ).
thf(463,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(5239,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)],[463]) ).
thf(1711,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(11254,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)],[1711]) ).
thf(720,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(6407,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)],[720]) ).
thf(2248,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(14429,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)],[2248]) ).
thf(1933,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(12636,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933]) ).
thf(418,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(5022,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)],[418]) ).
thf(1452,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(9952,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)],[1452]) ).
thf(16,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(2695,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)],[16]) ).
thf(45,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(2827,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)],[45]) ).
thf(2014,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(13132,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)],[2014]) ).
thf(1684,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(11149,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)],[1684]) ).
thf(1165,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(8601,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)],[1165]) ).
thf(1900,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_enumset1) ).
thf(12451,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(8497,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(921,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(7394,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)],[921]) ).
thf(2269,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(14502,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)],[2269]) ).
thf(632,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 ) ) )
& ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) )
=> ( ( D @ ( C @ k2_xboole_0 ) @ ( A @ k7_relat_1 ) )
= ( D @ ( C @ k2_xboole_0 ) @ ( B @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_relat_1) ).
thf(5965,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 ) ) )
& ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) )
=> ( ( D @ ( C @ k2_xboole_0 ) @ ( A @ k7_relat_1 ) )
= ( D @ ( C @ k2_xboole_0 ) @ ( B @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1989,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(12969,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)],[1989]) ).
thf(2577,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(15876,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)],[2577]) ).
thf(1792,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(11819,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(2515,axiom,
? [A: $i] :
( ( A @ v2_cat_5 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_cat_5) ).
thf(15630,plain,
? [A: $i] :
( ( A @ v2_cat_5 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2515]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_finseq_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_2) ).
thf(7425,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_finseq_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1632,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(10883,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)],[1632]) ).
thf(1664,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(11070,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)],[1664]) ).
thf(1907,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(12473,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)],[1907]) ).
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(13633,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(421,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(5033,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)],[421]) ).
thf(225,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(3964,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)],[225]) ).
thf(2235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( A @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_enumset1) ).
thf(14384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( A @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235]) ).
thf(1382,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(9587,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)],[1382]) ).
thf(1470,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(10034,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)],[1470]) ).
thf(2171,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(14074,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)],[2171]) ).
thf(272,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(4186,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)],[272]) ).
thf(1967,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(12845,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)],[1967]) ).
thf(714,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(6385,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)],[714]) ).
thf(708,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(6357,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)],[708]) ).
thf(416,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(5011,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)],[416]) ).
thf(2106,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(13673,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)],[2106]) ).
thf(1835,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(12067,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)],[1835]) ).
thf(383,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(4837,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(770,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(6667,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)],[770]) ).
thf(2519,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(15649,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)],[2519]) ).
thf(1481,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(10083,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)],[1481]) ).
thf(1505,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(10183,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)],[1505]) ).
thf(1661,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(11060,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)],[1661]) ).
thf(2158,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(14010,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_ens_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158]) ).
thf(174,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(3651,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)],[174]) ).
thf(1581,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(10640,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)],[1581]) ).
thf(1816,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(11951,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)],[1816]) ).
thf(267,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(4171,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)],[267]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( D @ ( F @ m2_finseq_1 ) )
=> ! [G: $i] :
( ( ( E @ ( D @ ( G @ m2_relset_1 ) ) )
& ( E @ ( D @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( F
= ( C @ ( B @ ( A @ k11_finseq_1 ) ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( D @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( G @ k1_funct_1 ) @ ( B @ ( G @ k1_funct_1 ) @ ( A @ ( G @ k1_funct_1 ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_finseq_2) ).
thf(8665,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( D @ ( F @ m2_finseq_1 ) )
=> ! [G: $i] :
( ( ( E @ ( D @ ( G @ m2_relset_1 ) ) )
& ( E @ ( D @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( F
= ( C @ ( B @ ( A @ k11_finseq_1 ) ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( D @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( G @ k1_funct_1 ) @ ( B @ ( G @ k1_funct_1 ) @ ( A @ ( G @ k1_funct_1 ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1843,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(12128,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)],[1843]) ).
thf(488,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(5331,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)],[488]) ).
thf(285,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(4236,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)],[285]) ).
thf(2211,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(14275,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)],[2211]) ).
thf(54,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(3002,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)],[54]) ).
thf(2057,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(13380,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)],[2057]) ).
thf(1697,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(11201,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)],[1697]) ).
thf(1523,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(10348,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)],[1523]) ).
thf(1171,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(8624,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)],[1171]) ).
thf(2484,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_partfun1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) )
<=> ( C @ ( D @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_pua2mss1) ).
thf(15428,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_partfun1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) )
=> ( C @ ( D @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484]) ).
thf(443,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(5148,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)],[443]) ).
thf(1369,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(9538,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)],[1369]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k10_pboole ) @ k2_funct_4 )
= ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ k10_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_functor0) ).
thf(7951,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k10_pboole ) @ k2_funct_4 )
= ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ k10_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1745,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(11515,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)],[1745]) ).
thf(1951,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(12748,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).
thf(1596,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(10728,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)],[1596]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k2_relat_1 @ r1_tarski ) )
& ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_4) ).
thf(2753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k2_relat_1 @ r1_tarski ) )
& ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) )
<=> ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_xboole_1) ).
thf(5207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(2508,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(15594,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)],[2508]) ).
thf(1895,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(12423,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)],[1895]) ).
thf(482,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(5314,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)],[482]) ).
thf(1372,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(9555,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)],[1372]) ).
thf(2493,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(15485,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)],[2493]) ).
thf(246,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(4060,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)],[246]) ).
thf(934,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(7465,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)],[934]) ).
thf(534,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(5539,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)],[534]) ).
thf(768,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(6636,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)],[768]) ).
thf(1419,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(9808,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(1875,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(12327,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)],[1875]) ).
thf(135,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(3416,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)],[135]) ).
thf(2281,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_partfun1 ) @ ( C @ ( A @ k4_partfun1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_partfun1) ).
thf(14549,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_partfun1 ) @ ( C @ ( A @ k4_partfun1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281]) ).
thf(2491,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(15470,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)],[2491]) ).
thf(1669,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(11085,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)],[1669]) ).
thf(580,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(5735,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)],[580]) ).
thf(1179,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 ) ) )
= ( C @ ( B @ ( A @ a_3_0_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_domain_1) ).
thf(8656,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 ) ) )
= ( C @ ( B @ ( A @ a_3_0_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(688,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(6248,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)],[688]) ).
thf(2217,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(14307,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)],[2217]) ).
thf(1570,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(10596,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)],[1570]) ).
thf(1417,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(9803,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)],[1417]) ).
thf(594,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(5784,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)],[594]) ).
thf(793,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(6757,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)],[793]) ).
thf(2474,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(15382,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)],[2474]) ).
thf(1085,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(8202,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)],[1085]) ).
thf(1525,axiom,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( A @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( A = k7_vectsp_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_vectsp_2) ).
thf(10361,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( A @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( A = k7_vectsp_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1869,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(12278,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)],[1869]) ).
thf(1931,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(12624,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)],[1931]) ).
thf(2560,axiom,
~ ( k3_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_qc_lang1) ).
thf(15789,plain,
~ ( k3_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2560]) ).
thf(1266,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(9089,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)],[1266]) ).
thf(691,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(6261,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)],[691]) ).
thf(2143,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(13903,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)],[2143]) ).
thf(1298,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(9248,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)],[1298]) ).
thf(2078,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(13531,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)],[2078]) ).
thf(2072,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(13482,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)],[2072]) ).
thf(758,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(6585,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)],[758]) ).
thf(181,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(3678,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)],[181]) ).
thf(1379,axiom,
! [A: $i,B: $i,C: $i,D: $i,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 ) )
=> ! [I: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( I @ r2_hidden ) )
=> ( ( H @ ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( G @ ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( F @ ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( E @ ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_mcart_1) ).
thf(9575,plain,
! [A: $i,B: $i,C: $i,D: $i,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 ) )
=> ! [I: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( I @ r2_hidden ) )
=> ( ( H @ ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( G @ ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( F @ ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( E @ ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_relat_1) ).
thf(5848,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(665,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(6112,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(2536,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(15701,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)],[2536]) ).
thf(1461,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(10000,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)],[1461]) ).
thf(1519,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(10316,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)],[1519]) ).
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 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).
thf(12369,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)],[1884]) ).
thf(1048,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(8042,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)],[1048]) ).
thf(1296,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(9243,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)],[1296]) ).
thf(2447,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(15237,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)],[2447]) ).
thf(2409,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_5_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p1_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_5_domain_1) ).
thf(15068,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p1_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_5_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_5_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p1_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2409]) ).
thf(788,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(6742,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)],[788]) ).
thf(123,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(3352,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)],[123]) ).
thf(1528,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(10370,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)],[1528]) ).
thf(755,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(6572,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)],[755]) ).
thf(2594,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(15978,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)],[2594]) ).
thf(1060,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] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m2_finseq_1 ) )
=> ( ( I
= ( G @ ( F @ ( E @ k11_finseq_1 ) ) ) )
=> ( ( I @ ( D @ ( H @ k5_funcop_1 ) ) )
= ( G @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_finseq_2) ).
thf(8088,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] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m2_finseq_1 ) )
=> ( ( I
= ( G @ ( F @ ( E @ k11_finseq_1 ) ) ) )
=> ( ( I @ ( D @ ( H @ k5_funcop_1 ) ) )
= ( G @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(169,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(3631,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)],[169]) ).
thf(948,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(7514,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)],[948]) ).
thf(1540,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_closure2) ).
thf(10429,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(798,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(6779,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(562,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(5671,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1317,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(9349,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)],[1317]) ).
thf(2361,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(14878,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)],[2361]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_mcart_1) ).
thf(8715,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1742,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(11508,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)],[1742]) ).
thf(1436,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(9867,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)],[1436]) ).
thf(433,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(5103,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)],[433]) ).
thf(2052,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(13343,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)],[2052]) ).
thf(1325,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(9377,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)],[1325]) ).
thf(2070,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(13467,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)],[2070]) ).
thf(729,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(6443,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)],[729]) ).
thf(1476,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(10066,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(1830,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(12034,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)],[1830]) ).
thf(182,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(3683,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)],[182]) ).
thf(1067,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(8120,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)],[1067]) ).
thf(1218,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k7_relat_1 ) )
= ( C @ ( A @ k7_relat_1 ) @ ( B @ ( A @ k7_relat_1 ) @ k1_funct_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_4) ).
thf(8831,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k7_relat_1 ) )
= ( C @ ( A @ k7_relat_1 ) @ ( B @ ( A @ k7_relat_1 ) @ k1_funct_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(929,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ k4_enumset1 ) ) ) ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_enumset1) ).
thf(7438,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ k4_enumset1 ) ) ) ) ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1636,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(10898,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)],[1636]) ).
thf(71,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(3106,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)],[71]) ).
thf(1274,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(9118,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)],[1274]) ).
thf(1287,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(9185,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)],[1287]) ).
thf(2309,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_cqc_lang ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cqc_lang) ).
thf(14664,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_cqc_lang ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309]) ).
thf(2084,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(13588,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)],[2084]) ).
thf(1713,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(11268,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)],[1713]) ).
thf(1471,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(10037,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)],[1471]) ).
thf(1050,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(8047,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)],[1050]) ).
thf(2141,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(13888,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)],[2141]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_partfun1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( E @ k1_relat_1 @ r1_tarski ) )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_partfun1) ).
thf(4586,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( E @ k1_relat_1 @ r1_tarski ) )
& ( 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 ) )
& ( A @ ( E @ k1_relat_1 @ r1_tarski ) )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) )
=> ( C
= ( B @ ( A @ k4_partfun1 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_partfun1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( E @ k1_relat_1 @ r1_tarski ) )
& ( 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 ) )
& ( A @ ( E @ k1_relat_1 @ r1_tarski ) )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1099,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(8269,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)],[1099]) ).
thf(2067,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(13422,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)],[2067]) ).
thf(405,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(4958,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)],[405]) ).
thf(279,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(4213,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)],[279]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(9015,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1465,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(10019,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)],[1465]) ).
thf(1138,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(8485,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)],[1138]) ).
thf(1607,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(10766,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)],[1607]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
thf(6154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(2558,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(15778,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)],[2558]) ).
thf(936,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 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).
thf(7470,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 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(2427,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(15155,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)],[2427]) ).
thf(2488,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(15455,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)],[2488]) ).
thf(304,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(4374,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k4_relat_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(2487,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( B @ ( A @ k5_ens_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ens_1) ).
thf(15453,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( B @ ( A @ k5_ens_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2487]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( B @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_mcart_1) ).
thf(8561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( B @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(128,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(3384,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)],[128]) ).
thf(635,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_ens_1 ) )
= ( C @ ( A @ k4_ens_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ k6_ens_1 ) ) @ ( A @ k4_ens_1 ) )
= ( B @ ( A @ k4_ens_1 ) ) )
& ( ( B @ ( C @ ( A @ k6_ens_1 ) ) @ ( A @ k3_ens_1 ) )
= ( C @ ( A @ k3_ens_1 ) ) )
& ( ( B @ ( C @ ( A @ k6_ens_1 ) ) @ k2_mcart_1 )
= ( B @ k2_mcart_1 @ ( C @ k2_mcart_1 @ k5_relat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_ens_1) ).
thf(5972,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_ens_1 ) )
= ( C @ ( A @ k4_ens_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ k6_ens_1 ) ) @ ( A @ k4_ens_1 ) )
= ( B @ ( A @ k4_ens_1 ) ) )
& ( ( B @ ( C @ ( A @ k6_ens_1 ) ) @ ( A @ k3_ens_1 ) )
= ( C @ ( A @ k3_ens_1 ) ) )
& ( ( B @ ( C @ ( A @ k6_ens_1 ) ) @ k2_mcart_1 )
= ( B @ k2_mcart_1 @ ( C @ k2_mcart_1 @ k5_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1355,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(9491,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)],[1355]) ).
thf(553,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k12_ens_1 )
= ( A @ k11_ens_1 @ ( A @ k10_ens_1 @ ( A @ k9_ens_1 @ ( A @ k8_ens_1 @ ( A @ k2_ens_1 @ ( A @ g1_cat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_ens_1) ).
thf(5616,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k12_ens_1 )
= ( A @ k11_ens_1 @ ( A @ k10_ens_1 @ ( A @ k9_ens_1 @ ( A @ k8_ens_1 @ ( A @ k2_ens_1 @ ( A @ g1_cat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1958,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(12780,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)],[1958]) ).
thf(2358,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(14865,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)],[2358]) ).
thf(1721,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(11306,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)],[1721]) ).
thf(2027,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(13204,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)],[2027]) ).
thf(1153,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(8556,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)],[1153]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k10_finseq_1 ) @ k4_card_3 @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ k10_finseq_1 ) ) )
& ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_6) ).
thf(4388,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ k10_finseq_1 ) ) )
& ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ k10_finseq_1 ) @ k4_card_3 @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k10_finseq_1 ) @ k4_card_3 @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ k10_finseq_1 ) ) )
& ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(2222,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(14337,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)],[2222]) ).
thf(1492,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(10136,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)],[1492]) ).
thf(1760,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(11630,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)],[1760]) ).
thf(1944,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(12697,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)],[1944]) ).
thf(1462,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(10004,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(2077,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(13529,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)],[2077]) ).
thf(1335,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(9407,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)],[1335]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(6969,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(147,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(3456,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)],[147]) ).
thf(95,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(3219,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)],[95]) ).
thf(1310,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(9302,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)],[1310]) ).
thf(1980,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(12926,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980]) ).
thf(1202,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(8735,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)],[1202]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_mcart_1) ).
thf(6165,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(2257,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(14458,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)],[2257]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E
= ( B @ ( A @ k10_finseq_1 ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( C @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( F @ k1_funct_1 ) @ ( A @ ( F @ k1_funct_1 ) @ k10_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_finseq_2) ).
thf(8192,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E
= ( B @ ( A @ k10_finseq_1 ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( C @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( F @ k1_funct_1 ) @ ( A @ ( F @ k1_funct_1 ) @ k10_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(2578,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(15880,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)],[2578]) ).
thf(2182,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(14122,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)],[2182]) ).
thf(43,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(2812,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)],[43]) ).
thf(2074,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(13499,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)],[2074]) ).
thf(28,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(2742,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)],[28]) ).
thf(2382,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(14979,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)],[2382]) ).
thf(314,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(4420,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)],[314]) ).
thf(2352,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(14839,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352]) ).
thf(318,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(4445,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)],[318]) ).
thf(1529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ k4_funct_4 ) ) ) ) )
=> ( ( ( D = F )
& ( C = E ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_4) ).
thf(10375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ k4_funct_4 ) ) ) ) )
=> ( ( ( D = F )
& ( C = E ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( A
!= ( A @ k2_mcart_1 ) )
& ( A
!= ( A @ k1_mcart_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_mcart_1) ).
thf(4009,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( A
!= ( A @ k2_mcart_1 ) )
& ( A
!= ( A @ k1_mcart_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1441,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(9888,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)],[1441]) ).
thf(1512,axiom,
! [A: $i] :
( ( A @ v1_realset1 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow13) ).
thf(10253,plain,
! [A: $i] :
( ( A @ v1_realset1 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(623,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(5894,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)],[623]) ).
thf(2317,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(14699,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)],[2317]) ).
thf(342,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(4569,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)],[342]) ).
thf(1833,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(12049,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)],[1833]) ).
thf(2131,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(13856,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)],[2131]) ).
thf(641,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(5994,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)],[641]) ).
thf(2153,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(13980,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)],[2153]) ).
thf(2481,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(15420,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)],[2481]) ).
thf(2367,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(14907,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)],[2367]) ).
thf(841,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(6989,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)],[841]) ).
thf(378,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(4818,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)],[378]) ).
thf(1831,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(12044,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).
thf(1245,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(8983,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)],[1245]) ).
thf(489,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(5335,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)],[489]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) @ ( C @ k3_cqc_lang ) )
= ( C @ k1_tarski @ ( B @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_7) ).
thf(5863,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) @ ( C @ k3_cqc_lang ) )
= ( C @ k1_tarski @ ( B @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(2391,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 @ m1_finseq_2 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( A @ ( C @ m1_finseq_2 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_finseq_2) ).
thf(15015,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 @ m1_finseq_2 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( A @ ( C @ m1_finseq_2 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391]) ).
thf(1001,axiom,
~ ( k5_numbers @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_card_4) ).
thf(7820,plain,
~ ( k5_numbers @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(707,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ( A @ ( B @ v3_card_fil ) ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
<=> ~ ( B @ ( A @ k2_card_fil ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_card_fil) ).
thf(6353,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ( A @ ( B @ v3_card_fil ) ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( B @ ( A @ k2_card_fil ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ~ ( B @ ( A @ k2_card_fil ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(395,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(4897,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)],[395]) ).
thf(1010,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_setfam_1 )
& ( A @ v1_setfam_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_setfam_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_setfam_1) ).
thf(7892,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_setfam_1 )
& ( A @ v1_setfam_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(411,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(4985,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)],[411]) ).
thf(549,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(5599,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)],[549]) ).
thf(1705,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(11233,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)],[1705]) ).
thf(2169,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(14063,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)],[2169]) ).
thf(2548,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(15745,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)],[2548]) ).
thf(2288,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(14576,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)],[2288]) ).
thf(1611,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(10778,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)],[1611]) ).
thf(1020,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(7928,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)],[1020]) ).
thf(2240,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(14402,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)],[2240]) ).
thf(993,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(7778,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(771,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(6678,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)],[771]) ).
thf(1247,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(8998,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)],[1247]) ).
thf(514,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(5466,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)],[514]) ).
thf(974,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(7675,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)],[974]) ).
thf(1360,axiom,
! [A: $i,B: $i] :
( ( ( B @ v2_membered )
& ( A @ v2_membered ) )
=> ( ( B @ ( A @ k5_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k5_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc43_membered) ).
thf(9511,plain,
! [A: $i,B: $i] :
( ( ( B @ v2_membered )
& ( A @ v2_membered ) )
=> ( ( B @ ( A @ k5_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k5_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(357,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v2_binop_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setwiseo) ).
thf(4726,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v2_binop_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1365,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(9528,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)],[1365]) ).
thf(1178,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(8652,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(2347,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_card_fil ) ) )
= ( C @ ( B @ ( A @ a_3_0_card_fil ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_card_fil) ).
thf(14824,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_card_fil ) ) )
= ( C @ ( B @ ( A @ a_3_0_card_fil ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347]) ).
thf(80,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(3150,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)],[80]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_enumset1 ) ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_enumset1) ).
thf(5838,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_enumset1 ) ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1925,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(12573,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)],[1925]) ).
thf(1124,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(8413,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)],[1124]) ).
thf(2313,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(14682,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)],[2313]) ).
thf(1942,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(12691,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).
thf(1734,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k5_mcart_1 ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_domain_1) ).
thf(11375,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = F ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k5_mcart_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k5_mcart_1 ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1916,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(12505,plain,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ( B @ v1_fraenkel ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(5775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(2229,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(14370,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)],[2229]) ).
thf(2570,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(15829,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)],[2570]) ).
thf(999,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(7805,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)],[999]) ).
thf(1017,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(7911,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)],[1017]) ).
thf(380,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(4827,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)],[380]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k2_relat_1 )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_4) ).
thf(8541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k2_relat_1 )
= ( D @ ( C @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(2566,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(15814,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)],[2566]) ).
thf(2302,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(14639,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)],[2302]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(6730,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1102,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(8280,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)],[1102]) ).
thf(1535,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(10402,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)],[1535]) ).
thf(1763,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(11643,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)],[1763]) ).
thf(2591,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(15960,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)],[2591]) ).
thf(1691,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(11173,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)],[1691]) ).
thf(2134,axiom,
f1_s10_fraenkel @ ( a_0_18_fraenkel @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s10_fraenkel) ).
thf(13867,plain,
f1_s10_fraenkel @ ( a_0_18_fraenkel @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134]) ).
thf(1223,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(8853,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)],[1223]) ).
thf(2086,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(13593,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)],[2086]) ).
thf(1128,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(8440,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)],[1128]) ).
thf(1703,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(11220,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)],[1703]) ).
thf(284,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(4232,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)],[284]) ).
thf(1390,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(9619,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)],[1390]) ).
thf(2095,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(13630,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)],[2095]) ).
thf(628,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(5931,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)],[628]) ).
thf(1351,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(9478,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)],[1351]) ).
thf(712,axiom,
( ( k1_numbers @ v2_membered )
& ( k1_numbers @ v1_membered )
& ~ ( k1_numbers @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_membered) ).
thf(6377,plain,
( ( k1_numbers @ v2_membered )
& ( k1_numbers @ v1_membered )
& ~ ( k1_numbers @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1161,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_xboole_1) ).
thf(8588,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(198,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(3759,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)],[198]) ).
thf(825,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(6907,plain,
! [A: $i] :
( ( A @ k12_funct_3 )
= ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ k13_funct_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(2542,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_card_fil )
= ( A @ a_1_0_card_fil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_card_fil) ).
thf(15725,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_card_fil )
= ( A @ a_1_0_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2542]) ).
thf(1344,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(9450,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)],[1344]) ).
thf(457,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(5218,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)],[457]) ).
thf(2334,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_classes2) ).
thf(14768,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334]) ).
thf(2360,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(14876,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)],[2360]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_partfun1) ).
thf(6394,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(1197,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(8719,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)],[1197]) ).
thf(6,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(2620,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)],[6]) ).
thf(1627,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(10852,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)],[1627]) ).
thf(1561,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(10549,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(1553,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(10514,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)],[1553]) ).
thf(2462,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(15326,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)],[2462]) ).
thf(2243,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_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 ) @ ( C @ ( B @ ( A @ k4_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 ) @ ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_realset1) ).
thf(14412,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_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 ) @ ( C @ ( B @ ( A @ k4_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 ) @ ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2243]) ).
thf(1839,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(12086,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)],[1839]) ).
thf(1404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_enumset1) ).
thf(9741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(518,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(5482,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)],[518]) ).
thf(2031,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(13236,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)],[2031]) ).
thf(1058,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(8084,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1674,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(11102,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)],[1674]) ).
thf(908,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(7334,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)],[908]) ).
thf(1757,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(11605,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)],[1757]) ).
thf(1437,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(9871,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)],[1437]) ).
thf(1641,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(10930,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)],[1641]) ).
thf(662,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(6100,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)],[662]) ).
thf(78,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(3142,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)],[78]) ).
thf(1726,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(11342,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)],[1726]) ).
thf(916,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(7366,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(275,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(4196,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)],[275]) ).
thf(1565,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k4_partfun1 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_partfun1) ).
thf(10576,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k4_partfun1 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(1469,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(10031,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)],[1469]) ).
thf(2195,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(14194,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)],[2195]) ).
thf(1446,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(9921,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)],[1446]) ).
thf(329,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relat_1) ).
thf(4497,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ k10_finseq_1 ) )
!= ( E @ ( D @ ( C @ k11_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_finseq_3) ).
thf(3348,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ k10_finseq_1 ) )
!= ( E @ ( D @ ( C @ k11_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(429,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(5089,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)],[429]) ).
thf(521,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(5495,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)],[521]) ).
thf(1695,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(11193,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)],[1695]) ).
thf(486,axiom,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(5326,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_enumset1) ).
thf(7507,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(2375,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(14947,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)],[2375]) ).
thf(1280,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k5_xboole_0 ) @ r2_hidden ) ) ) ) )
=> ( A @ v4_finsub_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finsub_1) ).
thf(9150,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k5_xboole_0 ) @ r2_hidden ) ) ) ) )
=> ( A @ v4_finsub_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(2357,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k4_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_funct_4) ).
thf(14862,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k4_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357]) ).
thf(2115,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(13737,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)],[2115]) ).
thf(1009,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(7884,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)],[1009]) ).
thf(931,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(7458,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)],[931]) ).
thf(1746,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(11535,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)],[1746]) ).
thf(1730,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(11361,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)],[1730]) ).
thf(51,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(2984,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)],[51]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( ( B @ v2_membered )
& ( A @ v2_membered ) )
=> ( ( B @ ( A @ k2_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k2_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc23_membered) ).
thf(6736,plain,
! [A: $i,B: $i] :
( ( ( B @ v2_membered )
& ( A @ v2_membered ) )
=> ( ( B @ ( A @ k2_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k2_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1358,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(9503,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)],[1358]) ).
thf(1131,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(8457,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)],[1131]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( ( k2_qc_lang1 @ ( B @ m1_subset_1 ) )
& ( k4_qc_lang1 @ ( A @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k6_cqc_lang ) )
= ( B @ ( A @ k3_cqc_lang ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_cqc_lang) ).
thf(5619,plain,
! [A: $i,B: $i] :
( ( ( k2_qc_lang1 @ ( B @ m1_subset_1 ) )
& ( k4_qc_lang1 @ ( A @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k6_cqc_lang ) )
= ( B @ ( A @ k3_cqc_lang ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_enumset1) ).
thf(9001,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(2056,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ k2_ens_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k9_ens_1 ) )
<=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k2_ens_1 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k4_ens_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_ens_1) ).
thf(13371,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ k2_ens_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k2_ens_1 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k4_ens_1 ) ) ) )
=> ( B
= ( A @ k9_ens_1 ) ) )
& ( ( B
= ( A @ k9_ens_1 ) )
=> ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k2_ens_1 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k4_ens_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).
thf(940,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(7490,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)],[940]) ).
thf(866,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(7102,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)],[866]) ).
thf(677,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(6170,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)],[677]) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k5_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k5_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_5) ).
thf(5812,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k5_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k5_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(6838,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1273,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( B @ k2_mcart_1 @ m2_relset_1 ) ) )
& ( B @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( B @ k2_mcart_1 @ v1_funct_2 ) ) )
& ( B @ k2_mcart_1 @ v1_funct_1 )
& ~ ( ( ( B @ ( A @ k3_ens_1 ) )
!= k1_xboole_0 )
& ( ( B @ ( A @ k4_ens_1 ) )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_ens_1) ).
thf(9111,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( B @ k2_mcart_1 @ m2_relset_1 ) ) )
& ( B @ ( A @ k4_ens_1 ) @ ( B @ ( A @ k3_ens_1 ) @ ( B @ k2_mcart_1 @ v1_funct_2 ) ) )
& ( B @ k2_mcart_1 @ v1_funct_1 )
& ~ ( ( ( B @ ( A @ k3_ens_1 ) )
!= k1_xboole_0 )
& ( ( B @ ( A @ k4_ens_1 ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(513,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(5463,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)],[513]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(5548,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1269,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(9097,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(278,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(4207,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)],[278]) ).
thf(2416,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(15107,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2416]) ).
thf(2038,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(13268,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)],[2038]) ).
thf(143,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(3444,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)],[143]) ).
thf(1855,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(12207,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)],[1855]) ).
thf(630,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(5959,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1240,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(8954,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)],[1240]) ).
thf(1538,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(10417,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(545,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(5587,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)],[545]) ).
thf(2262,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 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_subset_1) ).
thf(14476,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 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262]) ).
thf(2017,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(13144,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)],[2017]) ).
thf(1517,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_ens_1 )
= ( A @ a_1_0_ens_1 @ k3_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ens_1) ).
thf(10311,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_ens_1 )
= ( A @ a_1_0_ens_1 @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(2363,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(14887,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363]) ).
thf(996,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(7788,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)],[996]) ).
thf(1766,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k10_classes2 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_classes2) ).
thf(11665,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k10_classes2 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(952,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(7526,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)],[952]) ).
thf(869,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(7117,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)],[869]) ).
thf(1265,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(9086,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)],[1265]) ).
thf(2318,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k1_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_urysohn1) ).
thf(14703,plain,
k1_numbers @ k1_zfmisc_1 @ ( k1_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318]) ).
thf(1579,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_classes2 ) )
= ( B @ k3_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_classes2) ).
thf(10632,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_classes2 ) )
= ( B @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(750,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(6542,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)],[750]) ).
thf(2132,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 ) ) ) ) ) ) ) )
= ( H @ k1_tarski @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_enumset1) ).
thf(13861,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 ) ) ) ) ) ) ) )
= ( H @ k1_tarski @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132]) ).
thf(2398,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_urysohn1) ).
thf(15038,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2398]) ).
thf(2159,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_pboole ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_pboole) ).
thf(14012,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_pboole ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159]) ).
thf(2389,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(15011,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)],[2389]) ).
thf(1506,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(10191,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)],[1506]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(7975,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1993,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(12978,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k2_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).
thf(1883,axiom,
f2_s18_fraenkel @ ( a_0_33_fraenkel @ r1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s18_fraenkel) ).
thf(12368,plain,
f2_s18_fraenkel @ ( a_0_33_fraenkel @ r1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883]) ).
thf(130,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(3395,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)],[130]) ).
thf(1301,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m4_realset1 ) )
& ~ ( A @ v1_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_realset1) ).
thf(9259,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m4_realset1 ) )
& ~ ( A @ v1_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(92,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(3206,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)],[92]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_enumset1) ).
thf(7298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1399,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(9695,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)],[1399]) ).
thf(84,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(3161,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)],[84]) ).
thf(1440,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] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m2_finseq_1 ) )
=> ( ( I
= ( F @ ( E @ ( D @ k11_finseq_1 ) ) ) )
=> ( ( G @ ( I @ ( H @ k4_funcop_1 ) ) )
= ( G @ ( F @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( G @ ( E @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_finseq_2) ).
thf(9884,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] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m2_finseq_1 ) )
=> ( ( I
= ( F @ ( E @ ( D @ k11_finseq_1 ) ) ) )
=> ( ( G @ ( I @ ( H @ k4_funcop_1 ) ) )
= ( G @ ( F @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( G @ ( E @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k11_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(179,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(3672,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)],[179]) ).
thf(1510,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(10249,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)],[1510]) ).
thf(2348,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(14827,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)],[2348]) ).
thf(2045,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(13293,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).
thf(1483,axiom,
! [A: $i] :
( ( k2_qc_lang1 @ ( k1_qc_lang1 @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k4_qc_lang1 @ ( k1_qc_lang1 @ ( B @ m2_subset_1 ) ) )
=> ( ( k1_qc_lang1 @ ( k4_qc_lang1 @ ( A @ ( B @ k3_cqc_lang ) @ m2_relset_1 ) ) )
& ( A @ ( B @ k3_cqc_lang ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_cqc_lang) ).
thf(10091,plain,
! [A: $i] :
( ( k2_qc_lang1 @ ( k1_qc_lang1 @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k4_qc_lang1 @ ( k1_qc_lang1 @ ( B @ m2_subset_1 ) ) )
=> ( ( k1_qc_lang1 @ ( k4_qc_lang1 @ ( A @ ( B @ k3_cqc_lang ) @ m2_relset_1 ) ) )
& ( A @ ( B @ k3_cqc_lang ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_funct_1 )
& ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_relat_1 )
& ~ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_7) ).
thf(6659,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_funct_1 )
& ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_relat_1 )
& ~ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1932,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(12627,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)],[1932]) ).
thf(1410,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(9777,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)],[1410]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_xboole_1) ).
thf(6751,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(1066,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
!= k1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ k1_funct_1 ) @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( ( B @ ( A @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G
= ( E @ ( A @ k10_pboole ) ) )
=> ( D @ ( C @ ( G @ ( B @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_functor0 ) ) ) ) ) @ m1_functor0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_functor0) ).
thf(8116,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
!= k1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ k1_funct_1 ) @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( ( B @ ( A @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G
= ( E @ ( A @ k10_pboole ) ) )
=> ( D @ ( C @ ( G @ ( B @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_functor0 ) ) ) ) ) @ m1_functor0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(2552,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s10_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B != f3_s10_funct_2 )
=> ( ( B @ ( A @ ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f5_s10_funct_2 ) ) ) )
& ( ( f3_s10_funct_2 @ ( A @ ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ k8_funct_2 ) ) ) )
= f4_s10_funct_2 )
& ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s10_funct_2) ).
thf(15757,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s10_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B != f3_s10_funct_2 )
=> ( ( B @ ( A @ ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f5_s10_funct_2 ) ) ) )
& ( ( f3_s10_funct_2 @ ( A @ ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ k8_funct_2 ) ) ) )
= f4_s10_funct_2 )
& ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s10_funct_2 @ ( f1_s10_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2552]) ).
thf(1546,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(10449,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)],[1546]) ).
thf(1977,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_card_fil ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_card_fil ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( B @ k5_subset_1 ) ) ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_card_fil) ).
thf(12903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_card_fil ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( B @ k5_subset_1 ) ) ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_card_fil ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_card_fil ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( B @ k5_subset_1 ) ) ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).
thf(2066,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(13416,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)],[2066]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(7897,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1108,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(8323,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)],[1108]) ).
thf(2426,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(15152,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)],[2426]) ).
thf(565,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(5678,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ ( A @ k6_relat_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).
thf(4566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(387,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(4859,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)],[387]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(8637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(753,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(6564,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)],[753]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ k1_binop_1 ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_altcat_1) ).
thf(4113,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ k1_binop_1 ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(6843,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1359,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(9507,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(557,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(5652,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)],[557]) ).
thf(2346,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(14810,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)],[2346]) ).
thf(1928,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k4_partfun1 ) @ ( C @ ( A @ k4_partfun1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_partfun1) ).
thf(12616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k4_partfun1 ) @ ( C @ ( A @ k4_partfun1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( B @ ( A @ k10_finseq_1 ) @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_finseq_3) ).
thf(4355,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k10_finseq_1 ) @ v2_funct_1 )
=> ( A != B ) )
& ( ( A != B )
=> ( B @ ( A @ k10_finseq_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(728,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(6440,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)],[728]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k3_ens_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_ens_1) ).
thf(6821,plain,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k3_ens_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(111,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(3292,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)],[111]) ).
thf(440,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ k2_tarski ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_enumset1) ).
thf(5133,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ k2_tarski ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(1780,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(11758,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)],[1780]) ).
thf(1464,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(10016,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)],[1464]) ).
thf(781,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(6719,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)],[781]) ).
thf(1943,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(12695,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)],[1943]) ).
thf(2314,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(14688,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)],[2314]) ).
thf(1572,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(10604,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)],[1572]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(5991,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1948,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(12740,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)],[1948]) ).
thf(817,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 @ ( A @ k4_ens_1 ) )
= C )
& ( ( D @ ( A @ k3_ens_1 ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ens_1) ).
thf(6875,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 ) )
=> ( ( ( ( ( D @ ( A @ k4_ens_1 ) )
= C )
& ( ( D @ ( A @ k3_ens_1 ) )
= B ) )
=> ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( ( D @ ( A @ k4_ens_1 ) )
= C )
& ( ( D @ ( A @ k3_ens_1 ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(2373,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(14934,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)],[2373]) ).
thf(2244,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(14417,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)],[2244]) ).
thf(1052,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(8056,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)],[1052]) ).
thf(857,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(7058,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)],[857]) ).
thf(1868,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(12271,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)],[1868]) ).
thf(196,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(3754,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)],[196]) ).
thf(2062,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(13399,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)],[2062]) ).
thf(1190,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(8701,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)],[1190]) ).
thf(1621,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(10835,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)],[1621]) ).
thf(1116,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(8350,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)],[1116]) ).
thf(2461,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(15323,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)],[2461]) ).
thf(643,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(6012,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)],[643]) ).
thf(1704,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(11230,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)],[1704]) ).
thf(898,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(7283,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1480,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(10080,plain,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1876,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(12332,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)],[1876]) ).
thf(2213,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(14282,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213]) ).
thf(2216,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(14304,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)],[2216]) ).
thf(2180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( B @ ( D @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_enumset1) ).
thf(14111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( B @ ( D @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180]) ).
thf(1163,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(8592,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)],[1163]) ).
thf(127,axiom,
( ( k8_vectsp_2 = k1_xboole_0 )
& ( ( k1_xboole_0 @ ( k7_vectsp_2 @ k1_funct_1 ) )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k2_midsp_1 @ k1_binop_1 ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_grcat_1) ).
thf(3376,plain,
( ( k8_vectsp_2 = k1_xboole_0 )
& ( ( k1_xboole_0 @ ( k7_vectsp_2 @ k1_funct_1 ) )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k2_midsp_1 @ k1_binop_1 ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_mcart_1) ).
thf(5822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1941,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(12684,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)],[1941]) ).
thf(1037,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(8003,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1199,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(8725,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)],[1199]) ).
thf(1965,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(12839,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)],[1965]) ).
thf(2254,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(14449,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)],[2254]) ).
thf(873,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(7166,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)],[873]) ).
thf(1207,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(8772,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)],[1207]) ).
thf(2231,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(14374,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)],[2231]) ).
thf(1587,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(10685,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)],[1587]) ).
thf(2580,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(15905,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)],[2580]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( A @ ( C @ k4_finseq_2 ) )
= ( B @ ( D @ k4_finseq_2 ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pralg_1) ).
thf(3507,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( A @ ( C @ k4_finseq_2 ) )
= ( B @ ( D @ k4_finseq_2 ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1114,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(8345,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)],[1114]) ).
thf(1751,axiom,
( ( k5_urysohn1 @ v2_membered )
& ( k5_urysohn1 @ v1_membered )
& ~ ( k5_urysohn1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_urysohn1) ).
thf(11573,plain,
( ( k5_urysohn1 @ v2_membered )
& ( k5_urysohn1 @ v1_membered )
& ~ ( k5_urysohn1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(1747,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(11540,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)],[1747]) ).
thf(2023,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(13181,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)],[2023]) ).
thf(1489,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(10112,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)],[1489]) ).
thf(652,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(6051,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)],[652]) ).
thf(1779,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(11753,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)],[1779]) ).
thf(437,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(5125,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)],[437]) ).
thf(2338,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(14775,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)],[2338]) ).
thf(1847,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(12139,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)],[1847]) ).
thf(497,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(5388,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)],[497]) ).
thf(1192,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(8707,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)],[1192]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
thf(5399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(303,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(4366,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)],[303]) ).
thf(2283,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(14562,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)],[2283]) ).
thf(1135,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(8466,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
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 ) )
=> ( ( 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(12313,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)],[1873]) ).
thf(2265,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(14485,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)],[2265]) ).
thf(2010,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(13121,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)],[2010]) ).
thf(2121,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(13759,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)],[2121]) ).
thf(636,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(5980,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)],[636]) ).
thf(856,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(7045,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)],[856]) ).
thf(528,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(5523,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)],[528]) ).
thf(2036,axiom,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).
thf(13261,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).
thf(97,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(3228,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)],[97]) ).
thf(1755,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(11594,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)],[1755]) ).
thf(1233,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(8904,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)],[1233]) ).
thf(1798,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k6_classes2 ) ) )
= ( C @ ( B @ k4_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_classes2) ).
thf(11855,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k6_classes2 ) ) )
= ( C @ ( B @ k4_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(1062,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(8096,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)],[1062]) ).
thf(1555,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(10521,plain,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k2_qc_lang1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(394,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(4894,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)],[394]) ).
thf(1920,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(12519,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)],[1920]) ).
thf(2414,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k4_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k4_finsub_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_finsub_1) ).
thf(15102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k4_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k4_finsub_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2414]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ k2_tarski ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( D @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( ( ( A @ k1_mcart_1 )
= C )
| ( ( A @ k1_mcart_1 )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_mcart_1) ).
thf(4377,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ k2_tarski ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( D @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( ( ( A @ k1_mcart_1 )
= C )
| ( ( A @ k1_mcart_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1522,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k7_mcart_1 ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_domain_1) ).
thf(10333,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = H ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k7_mcart_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k7_mcart_1 ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(2187,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(14158,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)],[2187]) ).
thf(984,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_sysrel) ).
thf(7724,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1213,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(8813,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)],[1213]) ).
thf(991,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(7756,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)],[991]) ).
thf(1498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ k1_enumset1 ) ) @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_enumset1) ).
thf(10159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ k1_enumset1 ) ) @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(1106,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(8295,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)],[1106]) ).
thf(1047,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(8039,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)],[1047]) ).
thf(14,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(2689,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)],[14]) ).
thf(2172,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(14081,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)],[2172]) ).
thf(1650,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(10994,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)],[1650]) ).
thf(309,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(4398,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)],[309]) ).
thf(185,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(3691,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)],[185]) ).
thf(209,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(3828,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)],[209]) ).
thf(474,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(5277,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)],[474]) ).
thf(30,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(2747,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)],[30]) ).
thf(1864,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(12256,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)],[1864]) ).
thf(2267,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(14491,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)],[2267]) ).
thf(2150,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_0_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( 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_0_domain_1) ).
thf(13957,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] :
( ( 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_0_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_0_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( 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)],[2150]) ).
thf(1053,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(8060,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)],[1053]) ).
thf(462,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(5235,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)],[462]) ).
thf(1122,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(8396,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)],[1122]) ).
thf(588,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finsub_1) ).
thf(5767,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(694,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(6280,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)],[694]) ).
thf(1644,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_finset_1) ).
thf(10952,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(971,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(7655,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)],[971]) ).
thf(893,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(7264,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)],[893]) ).
thf(649,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(6036,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)],[649]) ).
thf(1456,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_enumset1) ).
thf(9980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(505,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(5418,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)],[505]) ).
thf(927,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(7429,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)],[927]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k9_finseq_1 )
!= ( D @ ( C @ ( B @ k11_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_finseq_3) ).
thf(3818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k9_finseq_1 )
!= ( D @ ( C @ ( B @ k11_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_relat_1 )
= ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_relat_1 )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_cat_1) ).
thf(2700,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_relat_1 )
= ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_cat_1 ) ) @ k1_relat_1 )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1500,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(10164,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)],[1500]) ).
thf(2421,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(15127,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)],[2421]) ).
thf(1499,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(10162,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)],[1499]) ).
thf(193,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(3722,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)],[193]) ).
thf(1841,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(12124,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)],[1841]) ).
thf(2004,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(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 @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(1764,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(11650,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)],[1764]) ).
thf(2099,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(13645,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)],[2099]) ).
thf(2184,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(14130,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)],[2184]) ).
thf(2093,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(13617,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)],[2093]) ).
thf(625,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(5912,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)],[625]) ).
thf(1183,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(8669,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)],[1183]) ).
thf(2116,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(13742,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)],[2116]) ).
thf(1473,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(10055,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)],[1473]) ).
thf(1286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(9182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(1484,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(10095,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)],[1484]) ).
thf(2058,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(13384,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)],[2058]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(7522,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1718,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(11297,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)],[1718]) ).
thf(1362,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(9518,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)],[1362]) ).
thf(1629,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(10861,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)],[1629]) ).
thf(1371,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(9550,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)],[1371]) ).
thf(369,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(4768,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)],[369]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ k1_funct_4 ) )
= ( B @ ( A @ k2_xboole_0 ) @ k6_partfun1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_4) ).
thf(8216,plain,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ k1_funct_4 ) )
= ( B @ ( A @ k2_xboole_0 ) @ k6_partfun1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(1981,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(12932,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)],[1981]) ).
thf(1222,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(8845,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)],[1222]) ).
thf(1320,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(9358,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)],[1320]) ).
thf(540,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(5560,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)],[540]) ).
thf(2451,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(15256,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)],[2451]) ).
thf(1422,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(9815,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(1007,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(7879,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)],[1007]) ).
thf(420,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(5030,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)],[420]) ).
thf(445,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(5154,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)],[445]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(5309,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(199,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(3774,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)],[199]) ).
thf(2048,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(13320,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).
thf(2518,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_card_fil @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ m1_card_fil ) )
& ( A = C )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_card_fil) ).
thf(15640,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( B @ ( C @ m1_card_fil ) )
& ( A = C )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_card_fil @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_card_fil @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ m1_card_fil ) )
& ( A = C )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2518]) ).
thf(2272,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(14513,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) ) ) )
& ( ( ( A @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_sysrel) ).
thf(8071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) ) ) )
& ( ( ( A @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(414,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(5001,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)],[414]) ).
thf(1312,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(9313,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)],[1312]) ).
thf(287,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(4241,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)],[287]) ).
thf(1336,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(9413,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)],[1336]) ).
thf(1696,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(11198,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)],[1696]) ).
thf(2349,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(14832,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)],[2349]) ).
thf(1657,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_waybel_5 ) ) ) )
= ( D @ ( C @ k2_funcop_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_waybel_5) ).
thf(11034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_waybel_5 ) ) ) )
= ( D @ ( C @ k2_funcop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(161,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(3564,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)],[161]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_ens_1 ) )
= ( B @ k1_mcart_1 @ k1_mcart_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ens_1) ).
thf(4737,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_ens_1 ) )
= ( B @ k1_mcart_1 @ k1_mcart_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(2512,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(15613,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)],[2512]) ).
thf(843,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(6994,plain,
! [A: $i] :
( ( A @ k20_mcart_1 )
= ( A @ k2_mcart_1 @ k2_mcart_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(2190,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(14179,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)],[2190]) ).
thf(703,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(6330,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)],[703]) ).
thf(2279,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(14545,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)],[2279]) ).
thf(2285,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(14567,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)],[2285]) ).
thf(1625,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_classes2 ) )
= ( B @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_classes2) ).
thf(10846,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_classes2 ) )
= ( B @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(1995,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(12983,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)],[1995]) ).
thf(1292,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(9220,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)],[1292]) ).
thf(1328,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(9386,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)],[1328]) ).
thf(1485,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(10097,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)],[1485]) ).
thf(1495,axiom,
! [A: $i] :
( ( k1_xboole_0 @ k1_tarski @ ( A @ m1_subset_1 ) )
=> ( A = k8_vectsp_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_vectsp_2) ).
thf(10150,plain,
! [A: $i] :
( ( k1_xboole_0 @ k1_tarski @ ( A @ m1_subset_1 ) )
=> ( A = k8_vectsp_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(1134,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(8464,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)],[1134]) ).
thf(2233,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(14378,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233]) ).
thf(1922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
=> ( ( D @ ( C @ ( B @ ( A @ k1_cqc_lang ) ) ) )
= D ) )
& ( ( A = B )
=> ( ( D @ ( C @ ( B @ ( A @ k1_cqc_lang ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cqc_lang) ).
thf(12523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
=> ( ( D @ ( C @ ( B @ ( A @ k1_cqc_lang ) ) ) )
= D ) )
& ( ( A = B )
=> ( ( D @ ( C @ ( B @ ( A @ k1_cqc_lang ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).
thf(1442,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(9891,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)],[1442]) ).
thf(777,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(6701,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)],[777]) ).
thf(723,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(6415,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)],[723]) ).
thf(1006,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(7876,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)],[1006]) ).
thf(1693,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(11181,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)],[1693]) ).
thf(1353,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(9486,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)],[1353]) ).
thf(564,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(5675,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)],[564]) ).
thf(1558,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(10536,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)],[1558]) ).
thf(1899,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(12439,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)],[1899]) ).
thf(907,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(7331,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)],[907]) ).
thf(2301,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(14636,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)],[2301]) ).
thf(1467,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(10023,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)],[1467]) ).
thf(2379,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(14960,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)],[2379]) ).
thf(459,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(5223,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(1956,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(12771,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)],[1956]) ).
thf(72,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(3124,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)],[72]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( ( B @ ( E @ k1_funct_1 ) )
= D )
& ( ( A @ ( E @ k1_funct_1 ) )
= C )
& ( ( E @ k1_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funct_4) ).
thf(4133,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( ( B @ ( E @ k1_funct_1 ) )
= D )
& ( ( A @ ( E @ k1_funct_1 ) )
= C )
& ( ( E @ k1_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1514,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(10260,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)],[1514]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ k1_tarski @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_enumset1) ).
thf(7207,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) )
= ( E @ k1_tarski @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1633,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(10885,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)],[1633]) ).
thf(1151,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(8547,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)],[1151]) ).
thf(1156,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(8564,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)],[1156]) ).
thf(2207,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(14252,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)],[2207]) ).
thf(2584,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ k12_ens_1 @ ( B @ k12_ens_1 @ r1_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_ens_1) ).
thf(15925,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ k12_ens_1 @ ( B @ k12_ens_1 @ r1_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2584]) ).
thf(932,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( D @ m2_finseq_2 ) ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( E @ ( D @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_finseq_2) ).
thf(7461,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( D @ m2_finseq_2 ) ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( E @ ( D @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(409,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(4976,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)],[409]) ).
thf(2527,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(15677,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)],[2527]) ).
thf(2327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k12_classes2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_classes2) ).
thf(14755,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k12_classes2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2327]) ).
thf(1433,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(9851,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)],[1433]) ).
thf(890,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(7251,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)],[890]) ).
thf(1994,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(12980,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)],[1994]) ).
thf(1659,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_enumset1) ).
thf(11054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(1318,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(9353,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)],[1318]) ).
thf(2579,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(15890,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)],[2579]) ).
thf(1973,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(12868,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)],[1973]) ).
thf(332,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(4510,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)],[332]) ).
thf(364,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(4748,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)],[364]) ).
thf(524,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(5504,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)],[524]) ).
thf(20,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(2711,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)],[20]) ).
thf(412,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(4991,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)],[412]) ).
thf(2545,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(15736,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k1_funct_7 ) @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2545]) ).
thf(681,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(6213,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)],[681]) ).
thf(509,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(5453,plain,
! [A: $i,B: $i] :
( ( B @ v2_membered )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v2_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(2148,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(13951,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)],[2148]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_xboole_1) ).
thf(7163,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(263,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(4143,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)],[263]) ).
thf(2136,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(13870,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)],[2136]) ).
thf(2270,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(14507,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)],[2270]) ).
thf(1652,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(11005,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)],[1652]) ).
thf(1563,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(10568,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)],[1563]) ).
thf(1457,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_4) ).
thf(9983,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(2354,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r2_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_subset_1) ).
thf(14853,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2354]) ).
thf(277,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(4202,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)],[277]) ).
thf(1342,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(9442,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)],[1342]) ).
thf(1728,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(11351,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)],[1728]) ).
thf(460,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(5226,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)],[460]) ).
thf(1254,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(9019,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)],[1254]) ).
thf(60,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(3024,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)],[60]) ).
thf(1152,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(8552,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)],[1152]) ).
thf(574,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(5717,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)],[574]) ).
thf(224,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(3961,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)],[224]) ).
thf(1520,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(10320,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)],[1520]) ).
thf(1307,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(9274,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)],[1307]) ).
thf(1406,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(9747,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(2384,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(14992,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)],[2384]) ).
thf(1817,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(11957,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)],[1817]) ).
thf(2009,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(13119,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)],[2009]) ).
thf(2142,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(13897,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)],[2142]) ).
thf(1324,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(9374,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)],[1324]) ).
thf(82,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(3156,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)],[82]) ).
thf(942,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(7498,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)],[942]) ).
thf(1802,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(11879,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)],[1802]) ).
thf(1074,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(8151,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)],[1074]) ).
thf(548,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 @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_domain_1) ).
thf(5596,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 @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(2198,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(14202,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)],[2198]) ).
thf(2000,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(13076,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)],[2000]) ).
thf(1503,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(10178,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(983,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(7720,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)],[983]) ).
thf(56,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(3007,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)],[56]) ).
thf(2428,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(15159,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)],[2428]) ).
thf(2295,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(14607,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)],[2295]) ).
thf(2087,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(13595,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)],[2087]) ).
thf(255,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(4111,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)],[255]) ).
thf(838,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(6975,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)],[838]) ).
thf(1963,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(12829,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(1345,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(9453,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)],[1345]) ).
thf(2155,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(13994,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)],[2155]) ).
thf(842,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(6992,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)],[842]) ).
thf(610,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(5841,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)],[610]) ).
thf(313,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(4414,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)],[313]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
~ ( ( ( B @ ( A @ k2_xboole_0 ) @ k1_setfam_1 )
!= ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_setfam_1) ).
thf(8431,plain,
! [A: $i,B: $i] :
~ ( ( ( B @ ( A @ k2_xboole_0 ) @ k1_setfam_1 )
!= ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(2457,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(15283,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)],[2457]) ).
thf(1720,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(11302,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)],[1720]) ).
thf(1810,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(11921,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)],[1810]) ).
thf(1732,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ k1_enumset1 ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_enumset1) ).
thf(11369,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ k1_enumset1 ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(281,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_setwiseo ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setwiseo) ).
thf(4217,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_setwiseo ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(2125,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(13784,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)],[2125]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k4_relat_1 @ ( B @ k2_xboole_0 ) @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_sysrel) ).
thf(3452,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k4_relat_1 @ ( B @ k2_xboole_0 ) @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1978,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(12912,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)],[1978]) ).
thf(2263,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(14479,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)],[2263]) ).
thf(657,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(6068,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)],[657]) ).
thf(506,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(5421,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)],[506]) ).
thf(1911,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(12484,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)],[1911]) ).
thf(845,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(7007,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = G ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_mcart_1) ).
thf(5184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = G ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = G ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(886,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(7239,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)],[886]) ).
thf(348,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(4639,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)],[348]) ).
thf(1427,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(9834,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)],[1427]) ).
thf(2253,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(14447,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253]) ).
thf(34,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(2760,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)],[34]) ).
thf(915,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(7363,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)],[915]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( ( C
!= ( C @ k2_mcart_1 ) )
& ( C
!= ( C @ k1_mcart_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_mcart_1) ).
thf(3400,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( ( C
!= ( C @ k2_mcart_1 ) )
& ( C
!= ( C @ k1_mcart_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(220,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(3946,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)],[220]) ).
thf(2551,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(15754,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2551]) ).
thf(2167,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k12_ens_1 @ u2_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_ens_1) ).
thf(14058,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k12_ens_1 @ u2_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167]) ).
thf(1259,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(9046,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)],[1259]) ).
thf(77,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(3139,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)],[77]) ).
thf(2042,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(13284,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)],[2042]) ).
thf(2120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_1) ).
thf(13756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120]) ).
thf(2323,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(14732,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)],[2323]) ).
thf(1606,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(10754,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)],[1606]) ).
thf(2397,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(15035,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)],[2397]) ).
thf(858,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(7061,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)],[858]) ).
thf(1189,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(8698,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)],[1189]) ).
thf(1676,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(11123,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)],[1676]) ).
thf(1526,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(10364,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)],[1526]) ).
thf(2350,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_partfun1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pua2mss1) ).
thf(14834,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_partfun1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m1_pua2mss1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350]) ).
thf(2413,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(15099,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)],[2413]) ).
thf(370,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ! [B: $i] :
( ( B
= ( A @ k1_mcart_1 ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k4_tarski ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(4770,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k4_tarski ) ) )
=> ( B = C ) )
=> ( B
= ( A @ k1_mcart_1 ) ) )
& ( ( B
= ( A @ k1_mcart_1 ) )
=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k4_tarski ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(7316,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1548,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(10464,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)],[1548]) ).
thf(1397,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(9665,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)],[1397]) ).
thf(877,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(7177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(967,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(7627,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)],[967]) ).
thf(1438,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(9876,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)],[1438]) ).
thf(1490,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(10114,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)],[1490]) ).
thf(2003,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(13087,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)],[2003]) ).
thf(1411,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(9780,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)],[1411]) ).
thf(1550,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(10508,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)],[1550]) ).
thf(1014,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(7904,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)],[1014]) ).
thf(2191,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(14182,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)],[2191]) ).
thf(533,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(5536,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)],[533]) ).
thf(1329,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(9389,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(160,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k10_ens_1 ) )
<=> ( ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) )
=> ( ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ ( B @ k1_funct_1 ) )
= ( C @ ( D @ ( A @ k6_ens_1 ) ) ) ) ) ) )
& ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ r2_hidden ) )
<=> ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_ens_1) ).
thf(3533,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) )
=> ( ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ ( B @ k1_funct_1 ) )
= ( C @ ( D @ ( A @ k6_ens_1 ) ) ) ) ) ) )
& ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) )
=> ( B @ k1_relat_1 @ ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) ) ) ) ) ) )
=> ( B
= ( A @ k10_ens_1 ) ) )
& ( ( B
= ( A @ k10_ens_1 ) )
=> ( ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) )
=> ( ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ ( B @ k1_funct_1 ) )
= ( C @ ( D @ ( A @ k6_ens_1 ) ) ) ) ) ) )
& ! [C: $i] :
( ( A @ k2_ens_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) )
=> ( B @ k1_relat_1 @ ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( D @ ( C @ ( A @ k2_ens_1 @ ( A @ k2_ens_1 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( ( C @ ( A @ k3_ens_1 ) )
= ( D @ ( A @ k4_ens_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(2554,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(15768,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)],[2554]) ).
thf(2039,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(13271,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)],[2039]) ).
thf(2590,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(15957,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)],[2590]) ).
thf(144,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(3447,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)],[144]) ).
thf(1609,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(10774,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)],[1609]) ).
thf(2471,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(15366,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)],[2471]) ).
thf(959,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(7547,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)],[959]) ).
thf(2563,axiom,
~ ( k4_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_qc_lang1) ).
thf(15805,plain,
~ ( k4_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(8533,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1243,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(8962,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)],[1243]) ).
thf(1770,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_enumset1) ).
thf(11681,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(1497,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(10156,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)],[1497]) ).
thf(810,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(6835,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)],[810]) ).
thf(2502,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(15548,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)],[2502]) ).
thf(894,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(7271,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(2514,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_relset_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_relset_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( C @ ( B @ p1_s2_relset_1 ) ) ) ) )
& ( f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_relset_1) ).
thf(15625,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_relset_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_relset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s2_relset_1 ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( B @ p1_s2_relset_1 ) ) ) ) ) )
& ( f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2514]) ).
thf(2177,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(14098,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)],[2177]) ).
thf(2456,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(15277,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)],[2456]) ).
thf(253,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(4102,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)],[253]) ).
thf(121,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(3346,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)],[121]) ).
thf(233,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(4006,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)],[233]) ).
thf(2092,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(13615,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)],[2092]) ).
thf(2022,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(13178,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).
thf(1860,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(12226,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)],[1860]) ).
thf(1278,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(9141,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(68,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(3056,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)],[68]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ ( B @ k2_tarski ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( A @ k2_mcart_1 )
= D )
& ( ( ( A @ k1_mcart_1 )
= C )
| ( ( A @ k1_mcart_1 )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_mcart_1) ).
thf(2643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ ( B @ k2_tarski ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( A @ k2_mcart_1 )
= D )
& ( ( ( A @ k1_mcart_1 )
= C )
| ( ( A @ k1_mcart_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2453,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(15268,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)],[2453]) ).
thf(616,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(5860,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)],[616]) ).
thf(1361,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ k3_cqc_lang ) @ k1_funct_1 ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_cqc_lang) ).
thf(9515,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ k3_cqc_lang ) @ k1_funct_1 ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(2239,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(14393,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)],[2239]) ).
thf(2424,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(15144,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)],[2424]) ).
thf(2286,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(14571,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)],[2286]) ).
thf(63,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k4_finseq_2 ) )
= ( B @ ( A @ k2_finseq_1 @ k1_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_finseq_2) ).
thf(3039,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k4_finseq_2 ) )
= ( B @ ( A @ k2_finseq_1 @ k1_funct_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ? [E: $i] :
( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_mcart_1) ).
thf(9647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ? [E: $i] :
( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(203,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(3797,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)],[203]) ).
thf(1986,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(12957,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)],[1986]) ).
thf(472,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(5272,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(242,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(4042,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)],[242]) ).
thf(645,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(6023,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)],[645]) ).
thf(973,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ? [C: $i] :
( ( A @ ( C @ v3_card_fil ) )
& ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ m1_card_fil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_card_fil) ).
thf(7670,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ? [C: $i] :
( ( A @ ( C @ v3_card_fil ) )
& ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ m1_card_fil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(149,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(3465,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)],[149]) ).
thf(2565,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(15809,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)],[2565]) ).
thf(1400,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(9707,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)],[1400]) ).
thf(2188,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(14172,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)],[2188]) ).
thf(259,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(4121,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)],[259]) ).
thf(1112,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k4_ens_1 ) @ ( A @ k5_ens_1 ) @ ( B @ ( A @ k6_ens_1 ) ) )
= B )
& ( ( B @ ( B @ ( A @ k3_ens_1 ) @ ( A @ k5_ens_1 ) @ ( A @ k6_ens_1 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_ens_1) ).
thf(8337,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k4_ens_1 ) @ ( A @ k5_ens_1 ) @ ( B @ ( A @ k6_ens_1 ) ) )
= B )
& ( ( B @ ( B @ ( A @ k3_ens_1 ) @ ( A @ k5_ens_1 ) @ ( A @ k6_ens_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(2173,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(14083,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)],[2173]) ).
thf(1478,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(10072,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(1491,axiom,
a_0_0_pre_circ @ v1_finset_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_pre_circ) ).
thf(10135,plain,
a_0_0_pre_circ @ v1_finset_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(1822,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(12010,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)],[1822]) ).
thf(1590,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(10697,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)],[1590]) ).
thf(217,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(3864,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)],[217]) ).
thf(1778,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(11745,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)],[1778]) ).
thf(2504,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(15576,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)],[2504]) ).
thf(1005,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(7872,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)],[1005]) ).
thf(806,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(6818,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)],[806]) ).
thf(2582,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(15913,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)],[2582]) ).
thf(201,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(3789,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)],[201]) ).
thf(1209,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(8780,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)],[1209]) ).
thf(648,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(6030,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)],[648]) ).
thf(1040,axiom,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(8011,plain,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(322,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(4468,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)],[322]) ).
thf(754,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(6567,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)],[754]) ).
thf(1936,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(12662,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)],[1936]) ).
thf(439,axiom,
k1_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_numbers) ).
thf(5132,plain,
k1_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(2163,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(14041,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)],[2163]) ).
thf(1256,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(9029,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)],[1256]) ).
thf(847,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(7012,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(2013,axiom,
! [A: $i] :
( ( A @ k6_lattice5 )
= ( A @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ k1_enumset1 ) ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice5) ).
thf(13129,plain,
! [A: $i] :
( ( A @ k6_lattice5 )
= ( A @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ k1_enumset1 ) ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).
thf(119,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(3336,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)],[119]) ).
thf(508,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(5426,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)],[508]) ).
thf(1316,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(9343,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)],[1316]) ).
thf(374,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(4791,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)],[374]) ).
thf(2443,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(15228,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)],[2443]) ).
thf(195,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(3748,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)],[195]) ).
thf(461,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(5228,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)],[461]) ).
thf(2275,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(14522,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)],[2275]) ).
thf(1346,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(9459,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)],[1346]) ).
thf(2094,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(13627,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)],[2094]) ).
thf(1198,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(8722,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(826,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(6910,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)],[826]) ).
thf(155,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(3501,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)],[155]) ).
thf(2464,axiom,
! [A: $i] :
( ( ( A @ v4_orders_3 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_3 ) )
<=> ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_orders_3) ).
thf(15336,plain,
! [A: $i] :
( ( ( A @ v4_orders_3 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ m1_orders_3 ) ) )
& ( ( A @ ( B @ m1_orders_3 ) )
=> ( A @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2464]) ).
thf(1425,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(9824,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)],[1425]) ).
thf(382,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(4834,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)],[382]) ).
thf(2006,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(13097,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)],[2006]) ).
thf(76,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(3136,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)],[76]) ).
thf(1840,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(12113,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)],[1840]) ).
thf(1630,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(10870,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)],[1630]) ).
thf(2114,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(13733,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)],[2114]) ).
thf(2151,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(13969,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)],[2151]) ).
thf(774,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(6694,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)],[774]) ).
thf(2304,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_1_relset_2 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( A
= ( E @ ( F @ ( C @ ( B @ k8_relset_2 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_relset_2) ).
thf(14646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( A
= ( E @ ( F @ ( C @ ( B @ k8_relset_2 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_1_relset_2 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_1_relset_2 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( A
= ( E @ ( F @ ( C @ ( B @ k8_relset_2 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2304]) ).
thf(1653,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(11013,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)],[1653]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( B @ k9_finseq_1 @ k4_card_3 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A
= ( C @ k9_finseq_1 ) )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_6) ).
thf(3780,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( A
= ( C @ k9_finseq_1 ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ k9_finseq_1 @ k4_card_3 @ ( A @ r2_hidden ) ) )
& ( ( B @ k9_finseq_1 @ k4_card_3 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A
= ( C @ k9_finseq_1 ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1577,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(10627,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(1683,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(11145,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)],[1683]) ).
thf(1449,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(9940,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)],[1449]) ).
thf(2335,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(14770,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2335]) ).
thf(1992,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ v4_finsub_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finsub_1) ).
thf(12976,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ v4_finsub_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(1809,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( D @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_enumset1) ).
thf(11918,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( D @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).
thf(1534,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k12_ens_1 @ u1_cat_1 @ ( B @ ( A @ k13_ens_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_ens_1) ).
thf(10400,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k12_ens_1 @ u1_cat_1 @ ( B @ ( A @ k13_ens_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(2365,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ p1_s6_domain_1 )
<=> ( B @ p2_s6_domain_1 ) ) )
=> ( ( A @ a_1_5_domain_1 )
= ( A @ a_1_6_domain_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s6_domain_1) ).
thf(14891,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p2_s6_domain_1 )
=> ( B @ p1_s6_domain_1 ) )
& ( ( B @ p1_s6_domain_1 )
=> ( B @ p2_s6_domain_1 ) ) ) )
=> ( ( A @ a_1_5_domain_1 )
= ( A @ a_1_6_domain_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365]) ).
thf(1077,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(8172,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)],[1077]) ).
thf(1472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
~ ( ? [I: $i] :
( ? [J: $i] :
( ~ ( ( ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k11_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k10_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k9_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k8_mcart_1 ) ) ) ) ) ) )
& ( I = J )
& ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( J @ m1_subset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) ) )
& ( H != k1_xboole_0 )
& ( G != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_mcart_1) ).
thf(10040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
~ ( ? [I: $i] :
( ? [J: $i] :
( ~ ( ( ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k11_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k10_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k9_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k8_mcart_1 ) ) ) ) ) ) )
& ( I = J )
& ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( J @ m1_subset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) ) )
& ( H != k1_xboole_0 )
& ( G != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(570,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(5699,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)],[570]) ).
thf(693,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(6277,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)],[693]) ).
thf(2103,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(13659,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)],[2103]) ).
thf(949,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_fraenkel ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_fraenkel) ).
thf(7520,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_fraenkel ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(7,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(2623,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)],[7]) ).
thf(238,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(4025,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)],[238]) ).
thf(137,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(3420,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)],[137]) ).
thf(2069,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(13438,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)],[2069]) ).
thf(1552,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ r3_zfrefle1 ) )
=> ( B @ ( A @ r2_zfrefle1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfrefle1) ).
thf(10512,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ r3_zfrefle1 ) )
=> ( B @ ( A @ r2_zfrefle1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(1509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) )
<=> ! [F: $i] :
( ( E @ ( F @ r2_hidden ) )
<=> ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_enumset1) ).
thf(10210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) )
=> ( E @ ( F @ r2_hidden ) ) )
& ( ( E @ ( F @ r2_hidden ) )
=> ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) ) ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) )
=> ! [F: $i] :
( ( ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) )
=> ( E @ ( F @ r2_hidden ) ) )
& ( ( E @ ( F @ r2_hidden ) )
=> ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(1097,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(8253,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)],[1097]) ).
thf(2102,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(13656,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)],[2102]) ).
thf(2380,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(14970,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)],[2380]) ).
thf(186,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(3694,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)],[186]) ).
thf(1947,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(12730,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)],[1947]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setwiseo) ).
thf(2796,plain,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2097,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_enumset1) ).
thf(13637,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).
thf(2185,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(14138,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)],[2185]) ).
thf(531,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( G @ m2_finseq_2 ) ) )
=> ( D @ ( A @ k4_finseq_2 ) @ ( D @ ( E @ ( G @ ( F @ k4_funcop_1 ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_finseq_2) ).
thf(5532,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( G @ m2_finseq_2 ) ) )
=> ( D @ ( A @ k4_finseq_2 ) @ ( D @ ( E @ ( G @ ( F @ k4_funcop_1 ) ) @ m2_finseq_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1377,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k2_enumset1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_enumset1) ).
thf(9569,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k2_enumset1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(269,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k7_relat_1 ) )
= ( B @ ( A @ k1_funct_1 ) @ ( B @ k3_cqc_lang ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_7) ).
thf(4175,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k7_relat_1 ) )
= ( B @ ( A @ k1_funct_1 ) @ ( B @ k3_cqc_lang ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(153,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(3497,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)],[153]) ).
thf(695,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(6290,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)],[695]) ).
thf(2404,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(15052,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)],[2404]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_xboole_1) ).
thf(8388,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(2091,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(13610,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)],[2091]) ).
thf(166,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(3585,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)],[166]) ).
thf(140,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(3430,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)],[140]) ).
thf(667,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(6118,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)],[667]) ).
thf(593,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k7_cat_1 ) )
= ( B @ ( A @ k3_cqc_lang ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_cat_1) ).
thf(5781,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k7_cat_1 ) )
= ( B @ ( A @ k3_cqc_lang ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(2523,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(15667,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)],[2523]) ).
thf(1331,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(9393,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)],[1331]) ).
thf(367,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(4759,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)],[367]) ).
thf(1975,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_enumset1) ).
thf(12893,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).
thf(1414,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(9792,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)],[1414]) ).
thf(644,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(6018,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)],[644]) ).
thf(2176,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(14094,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)],[2176]) ).
thf(1599,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(10738,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)],[1599]) ).
thf(854,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(7039,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)],[854]) ).
thf(2122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_card_fil ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_card_fil ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( E @ ( F @ r1_tarski ) )
& ( D @ ( C @ ( B @ a_3_1_card_fil ) ) @ ( F @ r2_hidden ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_card_fil) ).
thf(13761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_card_fil ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( E @ ( F @ r1_tarski ) )
& ( D @ ( C @ ( B @ a_3_1_card_fil ) ) @ ( F @ r2_hidden ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_card_fil ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_card_fil ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( E @ ( F @ r1_tarski ) )
& ( D @ ( C @ ( B @ a_3_1_card_fil ) ) @ ( F @ r2_hidden ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122]) ).
thf(2113,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(13716,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)],[2113]) ).
thf(2520,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_6_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p2_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_6_domain_1) ).
thf(15653,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p2_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_6_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_6_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p2_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520]) ).
thf(1904,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(12463,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)],[1904]) ).
thf(1731,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(11366,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)],[1731]) ).
thf(2422,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(15139,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)],[2422]) ).
thf(2589,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(15950,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)],[2589]) ).
thf(1064,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(8102,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)],[1064]) ).
thf(1277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_mcart_1) ).
thf(9130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(748,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 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setwiseo) ).
thf(6536,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 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(689,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(6252,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)],[689]) ).
thf(2032,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(13239,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)],[2032]) ).
thf(619,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(5869,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)],[619]) ).
thf(2535,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(15699,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)],[2535]) ).
thf(2564,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( 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',s8_domain_1__e1_38__relset_2) ).
thf(15807,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( 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)],[2564]) ).
thf(546,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(5590,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)],[546]) ).
thf(2149,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(13954,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)],[2149]) ).
thf(1783,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k4_partfun1 ) @ ( C @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_partfun1) ).
thf(11772,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k4_partfun1 ) @ ( C @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(970,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(7644,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)],[970]) ).
thf(27,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(2739,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)],[27]) ).
thf(252,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ( ( A @ k2_mcart_1 @ ( A @ k1_mcart_1 @ k4_tarski ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_mcart_1) ).
thf(4098,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ( ( A @ k2_mcart_1 @ ( A @ k1_mcart_1 @ k4_tarski ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1914,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ ( B @ ( A @ k7_cat_1 ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k1_tarski @ ( B @ ( A @ k7_cat_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k7_cat_1 ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_cat_1) ).
thf(12491,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ ( B @ ( A @ k7_cat_1 ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k1_tarski @ ( B @ ( A @ k7_cat_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k7_cat_1 ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914]) ).
thf(1997,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(12989,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)],[1997]) ).
thf(735,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(6462,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)],[735]) ).
thf(453,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(5194,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)],[453]) ).
thf(739,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(6499,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)],[739]) ).
thf(2557,axiom,
! [A: $i] :
~ ( A @ k6_lattice5 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice5) ).
thf(15775,plain,
! [A: $i] :
~ ( A @ k6_lattice5 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557]) ).
thf(1429,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(9839,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)],[1429]) ).
thf(1193,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(8710,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)],[1193]) ).
thf(1638,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(10909,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(424,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(5051,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)],[424]) ).
thf(2189,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(14176,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189]) ).
thf(188,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(3705,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)],[188]) ).
thf(844,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(6997,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)],[844]) ).
thf(1402,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(9711,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)],[1402]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ k4_card_3 @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( E @ k11_finseq_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_6) ).
thf(5078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i,F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( E @ k11_finseq_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ k4_card_3 @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ k4_card_3 @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( E @ k11_finseq_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
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 ) )
=> ( ( 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(12213,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)],[1856]) ).
thf(390,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(4880,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)],[390]) ).
thf(2417,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ r2_zfrefle1 ) )
<=> ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ r1_zfrefle1 ) )
<=> ( C @ ( B @ r1_zfrefle1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfrefle1) ).
thf(15109,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_zfrefle1 ) )
=> ( C @ ( A @ r1_zfrefle1 ) ) )
& ( ( C @ ( A @ r1_zfrefle1 ) )
=> ( C @ ( B @ r1_zfrefle1 ) ) ) ) )
=> ( B @ ( A @ r2_zfrefle1 ) ) )
& ( ( B @ ( A @ r2_zfrefle1 ) )
=> ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_zfrefle1 ) )
=> ( C @ ( A @ r1_zfrefle1 ) ) )
& ( ( C @ ( A @ r1_zfrefle1 ) )
=> ( C @ ( B @ r1_zfrefle1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2417]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
thf(7946,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(2377,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(14952,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)],[2377]) ).
thf(400,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(4917,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)],[400]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
= ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_xboole_1) ).
thf(6055,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
= ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1736,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(11447,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(2065,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ k3_enumset1 ) ) ) ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_enumset1) ).
thf(13413,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 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ k3_enumset1 ) ) ) ) @ ( C @ ( B @ ( A @ k1_enumset1 ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).
thf(375,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(4794,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)],[375]) ).
thf(1088,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] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m2_finseq_1 ) )
=> ! [J: $i] :
( ( B @ ( J @ m2_finseq_1 ) )
=> ( ( ( J
= ( G @ ( F @ k10_finseq_1 ) ) )
& ( I
= ( E @ ( D @ k10_finseq_1 ) ) ) )
=> ( ( J @ ( I @ ( H @ k3_funcop_1 ) ) )
= ( G @ ( E @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k10_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_finseq_2) ).
thf(8209,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] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m2_finseq_1 ) )
=> ! [J: $i] :
( ( B @ ( J @ m2_finseq_1 ) )
=> ( ( ( J
= ( G @ ( F @ k10_finseq_1 ) ) )
& ( I
= ( E @ ( D @ k10_finseq_1 ) ) ) )
=> ( ( J @ ( I @ ( H @ k3_funcop_1 ) ) )
= ( G @ ( E @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( H @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ k10_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(924,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(7419,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)],[924]) ).
thf(2154,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) @ k3_tarski )
= ( B @ ( A @ a_2_0_borsuk_1 ) @ k3_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_borsuk_1) ).
thf(13991,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) @ k3_tarski )
= ( B @ ( A @ a_2_0_borsuk_1 ) @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154]) ).
thf(438,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(5129,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)],[438]) ).
thf(912,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(7355,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)],[912]) ).
thf(215,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(3860,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)],[215]) ).
thf(1946,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(12702,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)],[1946]) ).
thf(2528,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(15679,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)],[2528]) ).
thf(1294,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ~ ( ( B @ ( A @ r2_hidden ) )
<=> ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(9229,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( C @ ( A @ r2_hidden ) ) ) )
=> ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
=> ~ ( ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( C @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(598,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(5796,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)],[598]) ).
thf(1075,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(8162,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)],[1075]) ).
thf(1921,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(12520,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)],[1921]) ).
thf(1866,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(12267,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)],[1866]) ).
thf(947,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 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m2_finseq_1 ) )
=> ( ( ( H
= ( E @ ( B @ k12_finseq_1 ) ) )
& ( G
= ( D @ ( A @ k12_finseq_1 ) ) ) )
=> ( ( H @ ( G @ ( F @ k3_funcop_1 ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ k12_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_finseq_2) ).
thf(7510,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 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m2_finseq_1 ) )
=> ( ( ( H
= ( E @ ( B @ k12_finseq_1 ) ) )
& ( G
= ( D @ ( A @ k12_finseq_1 ) ) ) )
=> ( ( H @ ( G @ ( F @ k3_funcop_1 ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ k12_finseq_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(415,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(5004,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)],[415]) ).
thf(1888,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(12380,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)],[1888]) ).
thf(2079,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(13542,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)],[2079]) ).
thf(1681,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(11140,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)],[1681]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_sysrel) ).
thf(5268,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1886,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(12374,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)],[1886]) ).
thf(875,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(7171,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)],[875]) ).
thf(2071,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(13473,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)],[2071]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_xboole_1) ).
thf(8769,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(2035,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(13257,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)],[2035]) ).
thf(1234,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(8908,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)],[1234]) ).
thf(829,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(6925,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)],[829]) ).
thf(710,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(6361,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)],[710]) ).
thf(887,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(7242,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)],[887]) ).
thf(1801,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(11871,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)],[1801]) ).
thf(2119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( C @ ( D @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_enumset1) ).
thf(13753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( C @ ( D @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119]) ).
thf(1776,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(11722,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)],[1776]) ).
thf(70,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(3100,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)],[70]) ).
thf(211,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(3837,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)],[211]) ).
thf(494,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(5356,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)],[494]) ).
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(2604,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(2339,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(14779,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)],[2339]) ).
thf(2395,axiom,
! [A: $i] :
( ( ( A @ v5_grcat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_grcat_1 ) )
<=> ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m3_grcat_1) ).
thf(15027,plain,
! [A: $i] :
( ( ( A @ v5_grcat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ m3_grcat_1 ) ) )
& ( ( A @ ( B @ m3_grcat_1 ) )
=> ( A @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2395]) ).
thf(733,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(6456,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)],[733]) ).
thf(26,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(2736,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)],[26]) ).
thf(516,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(5477,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)],[516]) ).
thf(738,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(6490,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)],[738]) ).
thf(2200,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(14208,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)],[2200]) ).
thf(2147,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(13941,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)],[2147]) ).
thf(327,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(4491,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)],[327]) ).
thf(1107,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(8309,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)],[1107]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(7248,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(2298,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(14615,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)],[2298]) ).
thf(1651,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(10998,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)],[1651]) ).
thf(2444,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(15230,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)],[2444]) ).
thf(1532,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(10396,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)],[1532]) ).
thf(344,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(4579,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)],[344]) ).
thf(881,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(7210,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)],[881]) ).
thf(1347,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(9463,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)],[1347]) ).
thf(1139,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(8489,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)],[1139]) ).
thf(2226,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(14350,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)],[2226]) ).
thf(1315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ? [G: $i] :
( ? [H: $i] :
( ~ ( ( ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k7_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k6_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k5_mcart_1 ) ) ) ) ) )
& ( G = H )
& ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( H @ m1_subset_1 ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) ) )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_mcart_1) ).
thf(9331,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ? [G: $i] :
( ? [H: $i] :
( ~ ( ( ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k7_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k6_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k5_mcart_1 ) ) ) ) ) )
& ( G = H )
& ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( H @ m1_subset_1 ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) ) )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(2532,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(15690,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)],[2532]) ).
thf(1750,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(11563,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)],[1750]) ).
thf(585,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(5760,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)],[585]) ).
thf(319,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(4455,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(2111,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(13701,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)],[2111]) ).
thf(1918,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(12515,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)],[1918]) ).
thf(85,axiom,
! [A: $i] : ( A @ k9_finseq_1 @ v2_funct_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_finseq_3) ).
thf(3164,plain,
! [A: $i] : ( A @ k9_finseq_1 @ v2_funct_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(2387,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_3_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p1_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_3_domain_1) ).
thf(14999,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p1_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_3_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_3_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p1_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2387]) ).
thf(666,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(6114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(477,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(5290,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)],[477]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ v1_finseq_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_finset_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_finseq_1) ).
thf(4474,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ v1_finseq_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_finset_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1051,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k5_xboole_0 ) @ r2_hidden ) ) ) ) )
=> ( A @ v4_finsub_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finsub_1) ).
thf(8051,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k5_xboole_0 ) @ r2_hidden ) ) ) ) )
=> ( A @ v4_finsub_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1688,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(11162,plain,
! [A: $i,B: $i] :
( ( B @ v1_membered )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(5339,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(820,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(6889,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)],[820]) ).
thf(1709,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(11246,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)],[1709]) ).
thf(229,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(3982,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)],[229]) ).
thf(208,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(3822,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)],[208]) ).
thf(2586,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(15938,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)],[2586]) ).
thf(58,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(3015,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)],[58]) ).
thf(1686,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(11155,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)],[1686]) ).
thf(1815,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(11943,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)],[1815]) ).
thf(32,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(2751,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)],[32]) ).
thf(1954,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(12766,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)],[1954]) ).
thf(2307,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(14659,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)],[2307]) ).
thf(222,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(3956,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)],[222]) ).
thf(270,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(4178,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)],[270]) ).
thf(764,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(6627,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)],[764]) ).
thf(1348,axiom,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k4_ens_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_ens_1) ).
thf(9466,plain,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k4_ens_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(2353,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(14843,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)],[2353]) ).
thf(117,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(3328,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)],[117]) ).
thf(1616,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(10809,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(2145,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(13926,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)],[2145]) ).
thf(2420,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(15123,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)],[2420]) ).
thf(300,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(4350,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)],[300]) ).
thf(430,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(5092,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)],[430]) ).
thf(1413,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(9788,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)],[1413]) ).
thf(1087,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(8207,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)],[1087]) ).
thf(346,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(4631,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)],[346]) ).
thf(744,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(6520,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)],[744]) ).
thf(2480,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(15416,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)],[2480]) ).
thf(88,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(3177,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)],[88]) ).
thf(1871,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(12307,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)],[1871]) ).
thf(2366,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(14903,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)],[2366]) ).
thf(434,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(5105,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)],[434]) ).
thf(2165,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(14050,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)],[2165]) ).
thf(2202,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( ( A @ ( B @ v3_card_fil ) )
<=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k1_card_fil ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_card_fil) ).
thf(14214,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k1_card_fil ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v3_card_fil ) ) )
& ( ( A @ ( B @ v3_card_fil ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k1_card_fil ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202]) ).
thf(1237,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(8921,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)],[1237]) ).
thf(417,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(5019,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)],[417]) ).
thf(192,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(3716,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)],[192]) ).
thf(1741,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(11494,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)],[1741]) ).
thf(752,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(6558,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)],[752]) ).
thf(2245,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k12_ens_1 @ u2_cat_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ens_1) ).
thf(14422,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k12_ens_1 @ u2_cat_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245]) ).
thf(1749,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k6_mcart_1 ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_domain_1) ).
thf(11548,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = G ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k6_mcart_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k6_mcart_1 ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(2293,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(14600,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)],[2293]) ).
thf(690,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(6258,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)],[690]) ).
thf(1408,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(9752,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)],[1408]) ).
thf(1700,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(11209,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(2525,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(15673,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)],[2525]) ).
thf(1101,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(8277,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)],[1101]) ).
thf(2319,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(14704,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)],[2319]) ).
thf(21,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(2714,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)],[21]) ).
thf(422,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(5036,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)],[422]) ).
thf(2175,axiom,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset1) ).
thf(14090,plain,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175]) ).
thf(1854,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ a_2_0_borsuk_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ k3_tarski ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_borsuk_1) ).
thf(12198,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ k3_tarski ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_borsuk_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_borsuk_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ k3_tarski ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).
thf(1877,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(12335,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)],[1877]) ).
thf(1767,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(11668,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(1023,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(7943,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)],[1023]) ).
thf(240,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(4034,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)],[240]) ).
thf(2441,axiom,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_relset_1) ).
thf(15213,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2441]) ).
thf(772,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(6682,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)],[772]) ).
thf(1176,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_xboole_1) ).
thf(8648,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1626,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(10849,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)],[1626]) ).
thf(1656,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(11028,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)],[1656]) ).
thf(138,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(3424,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)],[138]) ).
thf(399,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(4912,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)],[399]) ).
thf(761,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(6612,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)],[761]) ).
thf(2576,axiom,
! [A: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( A @ m2_relset_1 ) ) )
=> ! [B: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( B @ m2_relset_1 ) ) )
=> ( ( ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) )
& ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_pua2mss1) ).
thf(15850,plain,
! [A: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( A @ m2_relset_1 ) ) )
=> ! [B: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( B @ m2_relset_1 ) ) )
=> ( ( ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ p1_s2_pua2mss1 ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) ) )
& ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ p1_s2_pua2mss1 ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2576]) ).
thf(1698,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(11204,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)],[1698]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_cqc_lang ) )
= ( B @ ( A @ k1_tarski @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_cqc_lang) ).
thf(6040,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_cqc_lang ) )
= ( B @ ( A @ k1_tarski @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(7291,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(2547,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(15741,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)],[2547]) ).
thf(450,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(5176,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)],[450]) ).
thf(212,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ( ( A
!= ( A @ k2_mcart_1 ) )
& ( A
!= ( A @ k1_mcart_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_mcart_1) ).
thf(3843,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ( ( A
!= ( A @ k2_mcart_1 ) )
& ( A
!= ( A @ k1_mcart_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_funct_1 )
& ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_4) ).
thf(8822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_funct_1 )
& ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1905,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(12466,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)],[1905]) ).
thf(1375,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).
thf(9564,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(476,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(5283,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)],[476]) ).
thf(699,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(6309,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)],[699]) ).
thf(1851,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(12175,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)],[1851]) ).
thf(1881,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_enumset1) ).
thf(12363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881]) ).
thf(1635,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10896,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(1089,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(8213,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)],[1089]) ).
thf(1969,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(12855,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)],[1969]) ).
thf(680,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(6205,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)],[680]) ).
thf(2208,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(14256,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)],[2208]) ).
thf(2406,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( A @ r2_zfrefle1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_zfrefle1) ).
thf(15059,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( A @ r2_zfrefle1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2406]) ).
thf(236,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(4019,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)],[236]) ).
thf(1290,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(9198,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)],[1290]) ).
thf(1019,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(7925,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)],[1019]) ).
thf(1803,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(11886,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)],[1803]) ).
thf(1184,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(8675,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)],[1184]) ).
thf(2378,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(14956,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)],[2378]) ).
thf(1706,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(11236,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)],[1706]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ k2_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_finseq_2) ).
thf(3244,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ k2_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1132,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(8460,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)],[1132]) ).
thf(1894,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(12420,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)],[1894]) ).
thf(24,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ m2_finseq_2 ) ) )
=> ( ( C @ k4_finseq_1 )
= ( A @ k2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_finseq_2) ).
thf(2731,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ m2_finseq_2 ) ) )
=> ( ( C @ k4_finseq_1 )
= ( A @ k2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1794,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(11826,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)],[1794]) ).
thf(2088,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(13599,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)],[2088]) ).
thf(956,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(7538,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)],[956]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_enumset1) ).
thf(5204,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ ( A @ k1_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(73,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(3128,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)],[73]) ).
thf(1735,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(11390,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)],[1735]) ).
thf(1434,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(9859,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)],[1434]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_finseq_2 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_finseq_2) ).
thf(8328,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_finseq_2 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_finseq_2 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(187,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(3701,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)],[187]) ).
thf(2521,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(15662,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)],[2521]) ).
thf(1845,axiom,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(12134,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).
thf(1712,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(11258,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)],[1712]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ k2_tarski ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_enumset1) ).
thf(5151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( G @ ( F @ k2_tarski ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(561,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(5668,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)],[561]) ).
thf(910,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(7338,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)],[910]) ).
thf(1564,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(10573,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)],[1564]) ).
thf(306,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(4382,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)],[306]) ).
thf(163,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ m2_finseq_2 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( D @ m2_finseq_2 ) ) )
=> ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( A @ k2_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_finseq_2) ).
thf(3570,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( C @ m2_finseq_2 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( D @ m2_finseq_2 ) ) )
=> ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( A @ k2_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1858,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(12220,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)],[1858]) ).
thf(133,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(3411,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)],[133]) ).
thf(2332,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(14764,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)],[2332]) ).
thf(2574,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(15845,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)],[2574]) ).
thf(1255,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(9023,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)],[1255]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
= ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(6435,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
= ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(2204,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(14225,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)],[2204]) ).
thf(258,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(4118,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)],[258]) ).
thf(2237,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(14390,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237]) ).
thf(2439,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(15204,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)],[2439]) ).
thf(1513,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(10255,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)],[1513]) ).
thf(775,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(6697,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)],[775]) ).
thf(2127,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(13837,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)],[2127]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
| ! [D: $i,E: $i] :
( A
!= ( E @ ( D @ k4_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_mcart_1) ).
thf(4484,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ k2_mcart_1 @ r2_hidden ) )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
| ! [D: $i,E: $i] :
( A
!= ( E @ ( D @ k4_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(475,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(5280,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)],[475]) ).
thf(1343,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 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ( ( G
= ( D @ ( A @ k12_finseq_1 ) ) )
=> ( ( E @ ( G @ ( F @ k4_funcop_1 ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ k12_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_finseq_2) ).
thf(9446,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 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ( ( G
= ( D @ ( A @ k12_finseq_1 ) ) )
=> ( ( E @ ( G @ ( F @ k4_funcop_1 ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ k12_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(1275,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(9124,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(2533,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 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).
thf(15694,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 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2533]) ).
thf(312,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(4410,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)],[312]) ).
thf(286,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 ) )
=> ( A @ ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ m2_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finseq_2) ).
thf(4239,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 ) )
=> ( A @ ( D @ ( C @ ( B @ k11_finseq_1 ) ) @ m2_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(685,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(6233,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)],[685]) ).
thf(941,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(7493,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)],[941]) ).
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(7708,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(660,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v3_binop_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setwiseo) ).
thf(6082,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v3_binop_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1722,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(11309,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)],[1722]) ).
thf(1127,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(8437,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)],[1127]) ).
thf(851,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(7025,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)],[851]) ).
thf(1516,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(10308,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(2296,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_classes2 ) ) )
= ( B @ ( C @ ( A @ k7_classes2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_classes2) ).
thf(14610,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_classes2 ) ) )
= ( B @ ( C @ ( A @ k7_classes2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2296]) ).
thf(1460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( ( B @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= D )
& ( ( A @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_4) ).
thf(9992,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( ( B @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= D )
& ( ( A @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
<=> ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setwiseo) ).
thf(7617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) )
& ( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(862,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(7088,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)],[862]) ).
thf(2383,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k7_classes2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k7_classes2) ).
thf(14988,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k7_classes2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383]) ).
thf(1493,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(10146,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)],[1493]) ).
thf(403,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(4936,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)],[403]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( ( D
!= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_mcart_1) ).
thf(5468,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( ( D
!= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1185,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(8680,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)],[1185]) ).
thf(13,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_binop_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_setwiseo) ).
thf(2687,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_binop_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2329,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(14759,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329]) ).
thf(1354,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(9489,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)],[1354]) ).
thf(1432,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(9848,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(2109,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(13689,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)],[2109]) ).
thf(1158,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(8570,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)],[1158]) ).
thf(1679,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(11135,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)],[1679]) ).
thf(2489,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(15457,plain,
f2_s1_group_5 @ k1_zfmisc_1 @ ( a_0_0_group_5 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2489]) ).
thf(2181,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(14114,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)],[2181]) ).
thf(1384,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(9600,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(2242,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( A @ k2_ens_1 @ ( A @ k8_ens_1 @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( A @ k8_ens_1 @ v1_funct_2 ) ) )
& ( A @ k8_ens_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_ens_1) ).
thf(14407,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( A @ k2_ens_1 @ ( A @ k8_ens_1 @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_ens_1 @ ( A @ k8_ens_1 @ v1_funct_2 ) ) )
& ( A @ k8_ens_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242]) ).
thf(2509,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(15597,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)],[2509]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ k17_mcart_1 )
= ( A @ k1_mcart_1 @ k1_mcart_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_mcart_1) ).
thf(4363,plain,
! [A: $i] :
( ( A @ k17_mcart_1 )
= ( A @ k1_mcart_1 @ k1_mcart_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1224,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(8857,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)],[1224]) ).
thf(920,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(7392,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)],[920]) ).
thf(1654,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(11021,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)],[1654]) ).
thf(1715,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_2) ).
thf(11276,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(2110,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(13697,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)],[2110]) ).
thf(350,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(4655,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)],[350]) ).
thf(2075,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(13505,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)],[2075]) ).
thf(1250,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m2_finseq_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D
= ( A @ k9_finseq_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= ( A @ ( E @ k1_funct_1 ) @ k9_finseq_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_finseq_2) ).
thf(9006,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m2_finseq_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D
= ( A @ k9_finseq_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= ( A @ ( E @ k1_funct_1 ) @ k9_finseq_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1556,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(10522,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)],[1556]) ).
thf(1412,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(9784,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)],[1412]) ).
thf(805,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(6810,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)],[805]) ).
thf(1244,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(8966,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)],[1244]) ).
thf(2315,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(14691,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)],[2315]) ).
thf(1123,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(8405,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)],[1123]) ).
thf(1874,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(12316,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)],[1874]) ).
thf(359,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(4734,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)],[359]) ).
thf(57,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(3013,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)],[57]) ).
thf(159,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(3526,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)],[159]) ).
thf(1187,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(8685,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)],[1187]) ).
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_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_funct_3 ) ) )
= ( C @ k1_funct_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_3) ).
thf(9558,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)],[1373]) ).
thf(1475,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(10060,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)],[1475]) ).
thf(1013,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(7900,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)],[1013]) ).
thf(1592,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(10706,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(1531,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(10389,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)],[1531]) ).
thf(1288,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(9188,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)],[1288]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(5172,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( A @ k2_mcart_1 )
= C )
& ( ( A @ k1_mcart_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_mcart_1) ).
thf(3950,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( A @ k2_mcart_1 )
= C )
& ( ( A @ k1_mcart_1 )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1482,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(10086,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)],[1482]) ).
thf(336,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(4520,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)],[336]) ).
thf(2218,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(14310,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)],[2218]) ).
thf(2401,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(15044,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)],[2401]) ).
thf(1618,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(10813,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)],[1618]) ).
thf(954,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(7531,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)],[954]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(5542,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(2430,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(15166,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)],[2430]) ).
thf(1710,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(11251,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)],[1710]) ).
thf(1117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(8363,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ k1_binop_1 ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_cqc_lang) ).
thf(3212,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ k1_binop_1 ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(556,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(5649,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)],[556]) ).
thf(1368,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(9536,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ k2_relat_1 )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_finseq_2) ).
thf(4723,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ k2_relat_1 )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(511,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(5458,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)],[511]) ).
thf(596,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(5789,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)],[596]) ).
thf(2247,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(14426,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)],[2247]) ).
thf(673,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(6145,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)],[673]) ).
thf(2201,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(14210,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)],[2201]) ).
thf(1311,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(9310,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)],[1311]) ).
thf(46,axiom,
! [A: $i,B: $i] :
~ ( ~ ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( C
= ( C @ k2_mcart_1 @ ( C @ k1_mcart_1 @ k4_tarski ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_mcart_1) ).
thf(2832,plain,
! [A: $i,B: $i] :
~ ( ~ ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( C
= ( C @ k2_mcart_1 @ ( C @ k1_mcart_1 @ k4_tarski ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1079,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(8179,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)],[1079]) ).
thf(2394,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(15024,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)],[2394]) ).
thf(2494,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(15489,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)],[2494]) ).
thf(1038,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(8006,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(542,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(5569,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)],[542]) ).
thf(2223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D
= ( C @ ( B @ ( A @ k9_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_2) ).
thf(14340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D
= ( C @ ( B @ ( A @ k9_funct_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223]) ).
thf(1913,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(12488,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)],[1913]) ).
thf(1814,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(11938,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)],[1814]) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(7274,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(6575,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( ( A @ k2_mcart_1 )
= D )
| ( ( A @ k2_mcart_1 )
= C ) )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_mcart_1) ).
thf(4423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( ( ( ( A @ k2_mcart_1 )
= D )
| ( ( A @ k2_mcart_1 )
= C ) )
& ( B @ ( A @ k1_mcart_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( A
= ( A @ k2_mcart_1 @ ( A @ k1_mcart_1 @ k4_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_mcart_1) ).
thf(4056,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
=> ( A
= ( A @ k2_mcart_1 @ ( A @ k1_mcart_1 @ k4_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(773,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(6686,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)],[773]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C != A )
& ( B != C )
& ( A != B ) )
<=> ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_finseq_3) ).
thf(4863,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v2_funct_1 )
=> ( ( C != A )
& ( B != C )
& ( A != B ) ) )
& ( ( ( C != A )
& ( B != C )
& ( A != B ) )
=> ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(766,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(6632,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)],[766]) ).
thf(2362,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(14884,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)],[2362]) ).
thf(273,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(4189,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)],[273]) ).
thf(579,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(5732,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)],[579]) ).
thf(1836,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(12070,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)],[1836]) ).
thf(1743,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(11511,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)],[1743]) ).
thf(1299,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(9254,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1799,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k4_finsub_1 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_finsub_1) ).
thf(11858,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k4_finsub_1 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).
thf(902,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(7295,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)],[902]) ).
thf(2541,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(15722,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)],[2541]) ).
thf(1604,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(10750,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)],[1604]) ).
thf(2166,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(14055,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)],[2166]) ).
thf(66,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( D @ m2_finseq_2 ) ) )
=> ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( D @ m2_finseq_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_finseq_2) ).
thf(3047,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( A @ k4_finseq_2 ) @ ( C @ ( D @ m2_finseq_2 ) ) )
=> ( B @ ( A @ k4_finseq_2 ) @ ( B @ ( D @ m2_finseq_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1902,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(12456,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)],[1902]) ).
thf(782,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v1_classes2 )
& ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 )
& ( B @ ( A @ k2_xboole_0 ) @ v1_classes2 )
& ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_classes2) ).
thf(6722,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v1_classes2 )
& ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 )
& ( B @ ( A @ k2_xboole_0 ) @ v1_classes2 )
& ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1030,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(7970,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)],[1030]) ).
thf(1426,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(9831,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(112,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(3296,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)],[112]) ).
thf(2498,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(15516,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)],[2498]) ).
thf(232,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(4002,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)],[232]) ).
thf(26367,plain,
$false,
inference(e,[status(thm)],[15170,5857,12366,15752,4022,15380,5385,5810,5659,9929,13650,8536,5686,7304,13052,14782,7427,6387,8186,6405,14343,4094,5918,12055,2744,12607,5593,4909,5136,7569,6231,2778,13402,11372,14801,5329,14912,14404,8514,14463,15472,5320,4183,10730,11164,7660,7100,5390,3581,14220,14585,10743,6431,9076,8843,6121,3449,6448,5778,6555,11898,9864,6845,7072,6263,15413,14358,4728,6954,7285,4877,14932,9091,8828,10901,12699,12507,10790,9437,9032,6142,7940,10431,3153,12371,10711,5793,6602,11080,3185,15019,12458,15361,6791,6063,15066,4037,12949,10795,12030,7477,12426,14468,10446,8044,7358,6918,4500,14625,14748,14750,4515,12666,15671,7641,9604,10673,12376,9383,15770,15143,9901,3285,6798,14662,9918,10837,6776,13707,10314,5982,9059,8169,15981,13586,12896,5265,4215,7781,9572,15222,9400,4973,13845,15346,5529,15780,10694,5614,15579,9818,12013,6732,9950,5501,12971,9956,3648,7949,12742,2627,9356,10594,5412,3794,9644,4403,3439,14347,12939,6505,14602,11112,3049,3745,11072,12852,2607,14856,8635,15013,10103,8568,14519,13747,9052,6359,10358,12126,8622,3044,8913,7524,6127,13095,14273,4528,14694,11207,9261,15299,8519,15948,2933,9813,11962,15254,6515,9494,6634,6078,11513,5161,13298,13640,3313,6336,5178,15611,8650,8881,6804,15384,10414,9246,7980,15207,4980,14927,15514,15791,9540,7220,7168,7018,5935,15318,9195,5723,4137,13223,11831,10153,9946,7605,3370,11684,8911,11171,11449,10662,6466,5740,7064,3994,5393,8086,9845,2763,5486,8325,13127,11930,11907,11699,8816,6887,8578,12763,8133,12960,8256,12543,14488,14716,15688,6754,14328,6306,8025,6102,11340,14644,15077,4249,5342,15342,6707,13664,15033,3689,7822,2708,5274,6350,13553,5712,7386,12254,8610,14510,5765,14909,9056,4439,3976,14192,10935,14552,6892,5585,3938,9172,8500,4348,11068,12475,4743,7914,13679,14474,7277,5306,6242,3644,10630,7696,15387,2698,3131,4070,8225,9561,11817,9988,11913,10251,14277,12046,14088,7528,11299,7541,8834,14141,14440,8787,11178,8522,4130,6315,13776,8069,15394,7867,11812,6713,9805,9668,14391,5989,8022,13273,15943,3803,11628,8242,4428,14228,3713,4243,6130,11760,14002,14331,6502,13388,4265,15824,4471,12657,15199,12745,5744,9629,2691,3463,8590,9800,11981,5256,10534,2857,11463,5866,6470,5214,14376,4788,10687,8902,3638,5521,6905,14205,14455,6396,11100,5802,9155,7803,8819,8717,14773,9843,12137,6579,8468,12269,5622,5323,4928,4830,12621,6781,12229,6923,11132,12180,5851,9362,5829,14597,9240,5746,15684,9973,3708,14949,5076,13263,13350,3231,11959,8252,13332,6382,3258,12517,9266,8870,7733,7236,13134,4756,7226,8956,4903,5027,11293,6895,14547,11083,7015,9636,15105,11821,9298,10419,15500,12018,6840,12924,10746,11778,3966,11656,7894,15716,5526,9882,4173,10623,2996,7245,10591,3670,13744,7369,15748,11891,7441,6523,15246,7775,8791,9811,5680,6745,15623,11215,6176,3973,11838,15150,8659,8018,5805,5311,5985,3290,11793,15975,3093,6823,11708,8759,11971,13604,14387,6438,10734,5259,8196,15834,10602,3851,5059,8001,3036,14046,7473,5929,4718,14284,15712,15710,11312,7036,10670,12638,5773,15186,5353,9616,4842,8454,14372,9369,15458,6740,10551,13938,10833,7807,12824,14874,7336,4504,15774,7909,15008,15831,6347,5246,4307,8347,7954,12499,9035,10057,5897,12411,8691,3361,3756,2809,10106,2799,2639,10977,14798,12860,15738,15350,10932,6327,8443,11143,4707,3588,4892,7505,15321,14945,7688,5824,9272,8033,2718,3406,5970,9584,10029,8289,3510,4065,5695,8924,15235,14196,9440,3635,11545,5298,8123,3435,11677,14060,8751,12935,11597,14184,11159,9472,13526,7197,5174,5961,13671,13885,13286,7254,14730,7535,6529,14537,10725,14445,3857,6760,4199,10811,13386,12078,3303,4962,14836,8640,13848,3567,7022,10954,8927,8233,7745,3984,3169,3265,11791,9836,9004,4531,8365,15424,15179,12350,15449,6058,5968,15682,5545,13322,9797,13875,15697,5142,4557,7937,13233,8959,15920,8613,5562,10922,14263,15766,10911,15392,15258,4576,12132,12985,6884,8630,4031,4312,12073,14808,15518,7999,9175,9323,3418,10855,7110,10699,12664,10843,11074,3339,13547,9105,7730,8343,12437,10099,3261,4712,11582,12385,5611,7042,8783,11339,12613,6897,9522,3711,11238,7870,4016,10171,15734,6000,15843,14766,2596,3867,10975,11037,15434,6773,5579,5512,13186,8199,7881,14199,11484,11587,3022,5455,4252,7161,7710,14973,4091,15118,5366,15097,10409,8334,7084,14524,9126,4785,13218,14772,8081,3134,4821,5396,6178,10441,11212,6509,7906,4160,3664,11191,8878,3471,7301,7957,9177,10330,4053,5534,15638,7095,3282,9264,7097,8683,14680,13158,5769,9380,3958,4295,10263,14889,3166,13254,7977,13654,5879,5702,5655,10502,9217,4192,15050,3810,6848,8503,8145,14317,6427,6043,2820,6445,4994,11152,4947,3499,13924,3578,7361,5460,7503,6292,10583,6972,9626,9391,12025,7794,12618,13359,8181,5551,3144,6833,4746,5113,9423,10367,7501,10006,6392,13835,7713,15368,11670,14452,4740,6168,14565,11284,4104,10615,13681,5729,9613,8287,11702,4461,3667,12478,14100,10543,8136,3033,13153,10580,5515,4063,9095,6728,12016,4048,8884,9525,13074,4263,7750,8462,5854,7346,12353,8530,6748,7281,11356,3615,6413,12863,15826,12769,13116,5714,15243,3831,12264,5221,8545,3254,10748,3413,12404,2990,15714,6801,5270,7962,5673,5423,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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU429+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 09:45:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.59/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.90/2.51 % [INFO] Parsing done (1811ms).
% 6.90/2.55 % [INFO] Running in sequential loop mode.
% 7.53/2.93 % [INFO] eprover registered as external prover.
% 7.53/2.94 % [INFO] Scanning for conjecture ...
% 11.09/4.21 % [INFO] Found a conjecture (or negated_conjecture) and 19100 axioms. Running axiom selection ...
% 19.03/10.67 % [INFO] Axiom selection finished. Selected 2593 axioms (removed 16507 axioms).
% 23.16/12.88 % [INFO] Problem is first-order (TPTP FOF).
% 23.60/13.10 % [INFO] Type checking passed.
% 23.60/13.11 % [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 ...
% 109.28/54.84 % External prover 'e' found a proof!
% 109.28/54.85 % [INFO] Killing All external provers ...
% 109.28/54.85 % Time passed: 54356ms (effective reasoning time: 52291ms)
% 109.28/54.85 % 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)>
% 109.28/54.86 % Axioms used in derivation (2593): rc2_setfam_1, t106_xboole_1, t158_relat_1, t39_relset_1, t63_mcart_1, t44_xboole_1, t6_funct_7, t36_funcop_1, t119_funct_2, t60_mcart_1, t72_xboole_1, t189_relat_1, t60_funct_4, d5_monoid_0, t15_finset_1, t44_enumset1, t62_partfun1, redefinition_k2_card_fil, t23_funct_2, rc2_lopclset, t38_funct_4, t61_classes2, t75_funct_3, t1_filter_2, fc1_cqc_lang, dt_k11_classes2, fraenkel_a_0_0_altcat_2, dt_m2_pua2mss1, t42_xboole_1, dt_k1_funct_3, dt_k15_domain_1, t34_subset_1, t75_enumset1, t34_sysrel, t14_realset1, d1_enumset1, t76_funct_3, t10_funct_7, free_g2_quantal1, redefinition_m2_relset_1, t56_funct_3, idempotence_k1_finsub_1, t41_finseq_3, fraenkel_a_1_0_domain_1, t51_partfun1, s1_altcat_2, t68_enumset1, cc1_pre_circ, t5_fraenkel, t32_funcop_1, t92_enumset1, t21_zfmisc_1, t5_boole, t84_finseq_2, fc2_altcat_1, t133_finseq_2, t13_zfmisc_1, t30_funct_2, existence_m1_triang_1, t55_funcop_1, t10_lattice2, t13_relset_1, t70_setwiseo, t128_partfun1, t38_funcop_1, t4_functor0, t19_yellow_9, t131_partfun1, redefinition_k1_functor0, redefinition_k1_oppcat_1, fc4_finset_1, fraenkel_a_4_2_domain_1, t16_finsub_1, t79_mcart_1, dt_k2_borsuk_1, t4_grcat_1, t48_funcop_1, fraenkel_a_4_0_pua2mss1, fraenkel_a_3_2_domain_1, t4_cantor_1, dt_k11_binop_2, fc1_zfmisc_1, t15_card_4, t45_setwiseo, free_g1_group_1, t1_altcat_2, redefinition_k1_metric_1, t25_mcart_1, dt_k7_vectsp_2, t19_xboole_1, t99_relat_1, t82_enumset1, d17_vectsp_2, t177_orders_1, t42_cqc_lang, t12_borsuk_1, s2_filter_1, t17_xboole_1, t90_relat_1, t4_funct_4, t112_xboole_1, t130_partfun1, t42_subset_1, t55_mcart_1, t30_setwiseo, t43_subset_1, commutativity_k3_setwiseo, t15_setwiseo, d1_funcsdom, t14_cantor_1, cc2_finset_1, t7_multop_1, t20_zfmisc_1, t54_relat_1, t35_subset_1, rc2_triang_1, d1_tarski, t4_pre_circ, t101_relat_1, t135_zfmisc_1, t17_zfmisc_1, fc11_finseq_1, t3_pre_circ, fc3_finset_1, d3_mcart_1, dt_k3_cantor_1, s1_setwiseo, t8_altcat_1, t25_relset_1, d20_binop_1, t66_funct_2, t57_classes2, t11_yellow_9, t67_relat_1, t18_finsub_1, t66_partfun1, t4_closure2, dt_k9_funct_3, t154_relat_1, t53_setwiseo, d4_ens_1, d4_funct_1, t60_funcop_1, t49_setfam_1, t70_funct_2, t23_ens_1, t6_setfam_1, cc2_tex_2, t35_funct_2, t14_finset_1, t20_mcart_1, t85_enumset1, t53_subset_1, redefinition_k4_finsub_1, t19_mcart_1, t14_finseq_2, t1_funct_4, t63_funcop_1, dt_k8_funcop_1, t67_enumset1, dt_k4_relset_1, d14_binop_1, dt_k9_domain_1, dt_k5_relset_1, dt_k8_ens_1, d5_relat_1, t15_finseq_1, t105_zfmisc_1, rc6_grcat_1, redefinition_k6_funct_3, t140_zfmisc_1, t49_setwiseo, d2_cqc_lang, redefinition_k12_mcart_1, commutativity_k1_finsub_1, d9_setfam_1, t1_closure3, t109_xboole_1, t66_mcart_1, idempotence_k3_xboole_0, t5_ens_1, t67_funcop_1, d1_funct_5, rc4_finset_1, redefinition_k9_domain_1, t110_xboole_1, t57_funcop_1, t47_relset_1, t13_sysrel, dt_k4_finsub_1, t1_boole, t62_relat_1, t7_subset_1, t92_xboole_1, t84_mcart_1, t2_realset1, t32_funct_2, t3_lattice5, s6_domain_1, rc3_triang_1, t86_mcart_1, t38_mcart_1, t66_xboole_1, t23_xboole_1, 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, t85_mcart_1, t195_orders_1, t29_mcart_1, redefinition_k5_subset_1, t16_yellow_9, t20_funct_2, t134_finseq_2, fraenkel_a_1_1_ens_1, redefinition_k8_relset_2, d1_cqc_lang, d13_ens_1, t73_xboole_1, s1_yellow_3, redefinition_m2_finseq_2, t9_setfam_1, dt_k7_setwiseo, t3_xboole_1, t97_xboole_1, t24_mcart_1, t3_realset1, d3_subset_1, dt_m1_functor0, t98_relat_1, t18_funcop_1, t113_xboole_1, t42_sysrel, dt_m1_triang_1, t56_partfun1, t8_subset_1, t4_ordinal1, s3_funct_2, t45_funcop_1, fc1_functor0, cc1_setfam_1, fc1_xboole_0, t6_ens_1, t97_funct_3, t10_tops_2, t62_enumset1, t47_enumset1, t77_enumset1, t25_funct_1, t7_mcart_1, d10_realset1, t73_funct_4, t113_zfmisc_1, t140_partfun1, fc43_membered, t16_funct_2, dt_k7_domain_1, idempotence_k5_setwiseo, t7_lattice2, t27_setwiseo, t48_domain_1, t92_funct_3, t4_altcat_1, t34_xboole_1, t8_zfrefle1, t89_enumset1, dt_k7_subset_1, rc7_finseq_1, t91_relat_1, t88_mcart_1, t14_yellow_9, t111_zfmisc_1, dt_k2_subset_1, t64_funct_5, d4_funct_4, d1_lattice2, d4_urysohn1, involutiveness_k8_binop_2, t102_finseq_3, t38_funct_1, t62_classes2, t53_funct_2, t76_mcart_1, t29_borsuk_1, d5_tarski, t13_funct_7, rc1_borsuk_1, t6_funct_4, t83_mcart_1, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t37_funct_4, redefinition_k4_classes2, fc4_setfam_1, t156_funct_1, t101_xboole_1, t1_group_6, t59_partfun1, t72_funct_4, s12_funct_2, t53_funcop_1, t57_enumset1, t66_enumset1, t44_relat_1, fc4_funct_1, t1_subset, s3_filter_1, fraenkel_a_1_0_lattice5, redefinition_k7_funct_2, t147_relat_1, t10_partfun1, t158_partfun1, t12_yellow_9, dt_k2_card_fil, d5_xboole_0, dt_k7_relset_1, t32_mcart_1, t29_subset_1, d10_mcart_1, fc1_funct_4, t52_zfmisc_1, t144_relat_1, t57_domain_1, t33_setwiseo, t9_lattice2, fc4_subset_1, t71_funct_1, t10_mssubfam, dt_k2_cqc_lang, t22_funct_1, fc3_realset1, free_g3_vectsp_1, t83_funct_4, t9_borsuk_1, t79_funcop_1, fc1_numbers, dt_k3_funct_2, t31_funct_4, t74_funct_2, t168_funct_2, t43_xboole_1, fraenkel_a_8_0_domain_1, redefinition_k7_cat_1, t54_partfun1, t81_zfmisc_1, t16_fraenkel, t52_funct_4, fraenkel_a_0_0_pre_circ, t25_filter_1, fc3_functor0, t7_funct_2, d7_mcart_1, t10_relset_1, t135_partfun1, t55_domain_1, t146_funct_2, fc3_setfam_1, t10_funcop_1, t18_xboole_1, t42_setwiseo, t119_partfun1, t17_yellow_9, t36_sysrel, t4_funcop_1, d17_mcart_1, dt_k35_binop_2, t12_realset1, cc4_yellow21, t3_mcart_1, t78_funct_3, s23_fraenkel, t16_setwiseo, fc3_relat_1, t96_zfmisc_1, redefinition_k2_multop_1, t42_zfmisc_1, t18_cantor_1, t14_binop_1, dt_k9_relset_1, dt_k1_subset_1, t69_funct_3, t13_funcop_1, t6_xboole_1, t30_filter_1, t19_zfmisc_1, d8_funct_1, idempotence_k1_relset_2, dt_k5_urysohn1, t19_relat_1, t70_xboole_1, dt_m1_pua2mss1, d4_zfmisc_1, dt_k13_domain_1, dt_k2_urysohn1, t31_setwiseo, t33_mcart_1, t41_funct_2, t25_sysrel, t22_card_fil, t166_funct_2, t148_finseq_2, t11_altcat_1, t25_xboole_1, dt_m1_nat_lat, commutativity_k7_classes2, t1_qc_lang1, d9_monoid_0, redefinition_k9_classes2, t11_realset1, dt_k9_ens_1, t73_funcop_1, t47_relat_1, t148_partfun1, t36_partfun1, t53_funct_3, fc9_relat_1, t19_closure2, fc5_finset_1, t68_xboole_1, t21_membered, t41_mcart_1, d7_binop_1, t19_finset_1, t54_funct_4, t107_finseq_2, dt_k2_funct_4, t2_boole, dt_m1_filter_1, dt_k1_classes2, t35_zfmisc_1, t93_enumset1, t27_wellord2, t12_relset_2, d5_setfam_1, t28_funcop_1, t43_domain_1, t2_card_fil, t1_funcop_1, t11_pua2mss1, t82_relat_1, t20_yellow_9, t117_zfmisc_1, t29_funct_4, t65_partfun1, t186_partfun1, t44_funct_2, t5_yellow_6, free_g1_lattices, s1_filter_1, t16_finseq_1, involutiveness_k2_card_fil, t117_funct_1, dt_k4_realset1, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t27_xboole_1, s1_group_5, t122_zfmisc_1, t4_mcart_1, t14_sysrel, t15_funct_5, redefinition_k1_pcomps_1, existence_m1_filter_1, t98_funct_3, fc6_funcop_1, dt_m1_realset1, t110_zfmisc_1, t65_classes2, fc3_card_3, t3_pralg_1, fraenkel_a_1_4_domain_1, t24_relset_2, dt_k19_pralg_1, t64_domain_1, t43_zfmisc_1, fraenkel_a_0_0_yellow_3, t55_funct_4, t29_numbers, rc2_partfun1, t18_relat_1, cc1_fraenkel, t5_card_fil, t162_partfun1, dt_m3_pboole, dt_k6_partfun1, t95_enumset1, t103_zfmisc_1, redefinition_k3_pre_circ, t59_mcart_1, t95_zfmisc_1, fc1_urysohn1, t63_partfun1, t63_setwiseo, t91_finseq_2, t78_funcop_1, t15_relset_1, redefinition_k3_setwiseo, t20_funct_3, redefinition_k8_classes2, t13_ens_1, fraenkel_a_1_2_domain_1, existence_m1_pua2mss1, t104_enumset1, dt_k1_funct_7, t99_zfmisc_1, t44_mcart_1, t10_functor0, t2_functor1, t61_subset_1, d9_funct_1, free_g1_vectsp_1, rc3_funct_1, t81_xboole_1, t47_setfam_1, t49_funct_2, dt_k17_domain_1, dt_k5_domain_1, t17_membered, fc1_funct_1, existence_m2_finseq_2, t27_finseq_2, rc3_finseq_1, t7_orders_1, t104_finseq_3, t121_partfun1, rc1_fraenkel, t5_funct_7, t1_yellow_3, s5_filter_1, t6_mssubfam, rc2_finseq_1, t64_funcop_1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, t81_mcart_1, t51_enumset1, rc1_finseq_1, t57_funct_4, t9_cat_1, t50_funct_2, t63_domain_1, t75_funct_4, dt_k9_finseq_1, dt_m2_filter_1, rc4_triang_1, t70_zfmisc_1, t39_relat_1, dt_k3_metric_1, t69_zfmisc_1, t39_setwiseo, t10_metric_1, d7_partfun1, commutativity_k3_xboole_0, dt_k14_domain_1, t39_finseq_3, t25_setwiseo, t95_finseq_2, t56_relat_1, rc2_classes2, t93_funct_3, t41_relat_1, t27_zfmisc_1, t23_mcart_1, t84_funct_1, t18_ens_1, t37_xboole_1, t26_funct_2, t17_funct_1, t9_xboole_1, d1_card_fil, t82_funct_1, t59_subset_1, t41_zfmisc_1, fc2_functor0, dt_m2_relset_1, existence_m3_grcat_1, t10_borsuk_1, t9_mssubfam, t18_finset_1, t116_enumset1, t40_domain_1, t37_card_3, cc1_relat_1, t6_card_fil, t1_funct_3, dt_k7_funct_2, t131_zfmisc_1, d4_monoid_0, redefinition_k2_funct_2, t95_xboole_1, fraenkel_a_6_0_functor0, fc7_finseq_1, t11_funct_6, fc3_ens_1, t12_funct_5, idempotence_k5_subset_1, t50_zfmisc_1, t2_funct_1, t36_subset_1, fc8_finset_1, t16_funct_5, redefinition_k6_setfam_1, t40_finseq_2, t49_zfmisc_1, t45_yellow20, t102_relat_1, d17_ens_1, t1_waybel10, t42_yellow_9, t105_enumset1, t4_multop_1, t29_partfun1, t31_relset_1, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, dt_k2_realset1, commutativity_k7_domain_1, t49_enumset1, t70_partfun1, t88_finseq_2, d9_mcart_1, t3_funcop_1, fc28_membered, dt_k1_toler_1, t3_setfam_1, t130_funct_2, t152_funct_2, s13_funct_2, rc1_funct_1, d1_relset_2, t150_pboole, redefinition_m1_triang_1, d6_binop_1, t64_funct_2, t4_setwiseo, t15_mcart_1, t2_funct_6, t115_zfmisc_1, t52_funcop_1, existence_m2_card_fil, t62_funct_1, t76_funct_2, dt_k7_binop_2, t58_setwiseo, fraenkel_a_4_1_yellow_9, redefinition_k2_finsub_1, t80_funcop_1, t65_funct_2, fc30_membered, t19_funct_1, t56_setwiseo, t25_relset_2, fc42_membered, t68_mcart_1, free_g2_lattices, fc11_finset_1, dt_k14_mcart_1, t5_tex_2, dt_k8_relset_2, fraenkel_a_2_0_domain_1, t23_funct_7, t13_funct_4, d2_tarski, t24_funct_2, t29_finset_1, redefinition_k5_classes2, dt_k2_binop_1, t137_zfmisc_1, fraenkel_a_2_2_domain_1, t100_finseq_2, t129_zfmisc_1, d4_subset_1, t2_binop_1, t2_partfun1, t30_funcop_1, dt_k4_classes2, t86_xboole_1, involutiveness_k3_subset_1, t13_relat_1, t51_mcart_1, t89_xboole_1, redefinition_k14_domain_1, t83_funcop_1, t17_binop_1, redefinition_k2_cqc_lang, d1_fraenkel, t25_funct_2, fc2_xboole_0, fraenkel_a_4_0_domain_1, t11_finseq_2, t97_finseq_2, t15_binop_1, t26_finseq_1, dt_m2_realset1, t9_funct_3, t32_subset_1, t80_funct_3, t108_enumset1, dt_k32_binop_2, fraenkel_a_1_2_ens_1, t112_relat_1, t75_funct_2, t31_finset_1, t175_partfun1, t21_funct_4, t15_relat_1, t41_setwiseo, dt_k6_cqc_lang, t154_funct_2, t48_funct_2, fraenkel_a_3_7_domain_1, t12_funct_4, t49_mcart_1, t27_relat_1, t58_mcart_1, t156_funct_2, t18_funct_5, t78_funct_4, d1_xboole_0, t89_mcart_1, t71_funct_3, t5_mssubfam, free_g1_funcsdom, dt_m1_eqrel_1, t49_funct_1, d6_monoid_0, fc17_binop_2, cc7_tex_2, t108_xboole_1, dt_k4_finseq_1, t34_partfun1, s4_filter_1, d4_cantor_1, dt_k7_classes2, dt_k3_setwiseo, dt_k9_funct_2, s2_relset_1, redefinition_k1_nattra_1, t14_card_fil, t40_funct_1, redefinition_k8_funcop_1, t56_enumset1, t89_finseq_2, t2_mssubfam, t15_finsub_1, d2_tex_2, t29_setwiseo, t80_enumset1, t3_mssubfam, d7_ens_1, t2_zfrefle1, t3_waybel20, t64_relat_1, t138_zfmisc_1, rc6_finseq_1, t25_subset_1, t74_enumset1, fraenkel_a_2_0_borsuk_1, d5_urysohn1, t96_funct_3, t52_enumset1, d2_funcop_1, t16_pua2mss1, t12_functor0, t30_finset_1, d5_funcop_1, fraenkel_a_2_0_card_fil, fraenkel_a_1_5_domain_1, t23_funct_1, t130_zfmisc_1, t51_xboole_1, dt_k10_funcop_1, dt_k2_finsub_1, t20_functor0, t36_mcart_1, cc1_tex_2, t108_zfmisc_1, t96_relat_1, t28_funct_4, t165_funct_2, fc10_finset_1, t60_partfun1, t6_closure2, t56_zfmisc_1, t80_mcart_1, redefinition_m3_grcat_1, t27_relset_1, t12_mcart_1, t52_domain_1, t40_setwiseo, t102_finseq_2, t15_funcop_1, t79_funct_3, t11_pre_circ, t52_relset_1, dt_k8_classes2, t34_funct_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, s4_subset_1, t8_funct_2, dt_k4_setwiseo, t6_funct_3, t29_funct_2, t56_funct_4, dt_k4_ens_1, fraenkel_a_2_0_cantor_1, t118_funct_2, fc2_setfam_1, t126_partfun1, t14_relset_1, dt_m2_card_fil, dt_k1_card_fil, existence_m1_realset1, t26_finset_1, t73_funct_3, dt_k2_cat_5, t16_relset_1, t39_funct_4, fc3_lattice5, t107_enumset1, t53_relset_1, d6_enumset1, t30_sysrel, t6_mcart_1, redefinition_m1_orders_3, s1_funct_7, d3_enumset1, d13_relat_1, t46_zfmisc_1, t31_partfun1, t37_partfun1, dt_k2_relset_2, t171_partfun1, t164_funct_2, fc2_funct_2, t6_boole, t12_funct_1, t62_mcart_1, t10_funct_3, t4_orders_1, t67_setwiseo, t3_funct_2, t18_subset_1, t8_cat_1, dt_k1_functor0, rc2_subset_1, t1_closure2, fc9_finset_1, t46_mcart_1, t16_funct_7, t4_funct_5, t26_borsuk_1, t63_funct_1, t30_borsuk_1, t38_sysrel, t50_xboole_1, dt_k6_subset_1, t10_relat_1, t65_enumset1, t59_setfam_1, d1_relat_1, t24_finsub_1, existence_m2_pua2mss1, dt_k3_relset_2, t37_setwiseo, t185_partfun1, fraenkel_a_3_0_card_fil, t9_cantor_1, dt_k15_ens_1, d3_realset1, t1_funct_6, d6_mcart_1, t5_functor0, t55_relat_1, s17_fraenkel, redefinition_k13_mcart_1, t57_mcart_1, t1_xboole_1, redefinition_k4_relset_2, t87_mcart_1, redefinition_m1_nat_lat, t15_yellow_9, t26_relset_1, t72_relat_1, t66_funct_5, dt_k1_funct_4, t64_partfun1, fc3_cantor_1, t52_relat_1, t35_funcop_1, t77_funct_2, t59_domain_1, free_g1_pre_topc, dt_k5_ens_1, t20_funct_1, t82_finseq_2, t12_sysrel, rc2_waybel_7, dt_k4_card_fil, t104_relat_1, t28_wellord2, t69_funct_4, t39_funcop_1, fc1_fraenkel, d3_finseq_2, t32_relset_1, t17_domain_1, t7_setfam_1, t3_partfun1, dt_k10_binop_2, t59_setwiseo, t4_setfam_1, t39_finseq_2, t32_partfun1, redefinition_k4_funct_2, t56_yellow_0, t73_relat_1, t4_relat_1, fc5_funcop_1, t28_subset_1, t52_xboole_1, t185_relat_1, t21_finset_1, t44_finseq_2, t75_xboole_1, fraenkel_a_1_0_card_fil, fc17_finset_1, s5_domain_1, dt_k6_pralg_1, dt_k10_setwiseo, t34_funct_4, commutativity_k2_xboole_0, dt_k3_urysohn1, t15_domain_1, dt_k2_classes2, t128_zfmisc_1, t39_partfun1, t50_enumset1, t5_altcat_1, t142_finseq_2, fc3_subset_1, t5_subset, symmetry_r4_nattra_1, d9_realset1, t112_enumset1, dt_k9_classes2, t48_zfmisc_1, t7_mssubfam, t4_zfrefle1, t45_funct_2, t84_enumset1, existence_m1_cat_5, t100_enumset1, t25_zfmisc_1, d4_relat_1, t50_frechet2, t75_zfmisc_1, t94_zfmisc_1, t11_mcart_1, t8_mcart_1, t24_borsuk_1, t4_xboole_0, t41_funcop_1, d2_realset1, t81_enumset1, t32_sysrel, t3_functor0, t6_lattice2, d17_nattra_1, fc6_finset_1, free_g1_cat_1, t63_funct_5, t123_enumset1, t65_xboole_1, t43_funct_4, t122_partfun1, fraenkel_a_0_32_fraenkel, t1_triang_1, t38_card_3, t22_filter_1, fc17_finseq_1, t23_binop_1, d6_partfun1, t61_setwiseo, t150_relat_1, existence_m1_relset_1, t20_finseq_1, d11_mcart_1, d18_vectsp_2, commutativity_k5_subset_1, t55_setfam_1, t36_finseq_2, t1_zfmisc_1, t77_mcart_1, t68_funct_3, s8_domain_1, t46_partfun1, d2_enumset1, t12_setfam_1, t101_finseq_2, t3_funct_6, redefinition_k11_classes2, t5_setfam_1, t52_funct_1, d1_cantor_1, t163_relat_1, t28_mcart_1, s21_fraenkel, t3_fraenkel, t53_funct_4, rc3_setfam_1, t22_setwiseo, existence_m1_functor0, redefinition_k14_borsuk_1, t123_zfmisc_1, fc2_subset_1, t2_membered, t16_yellow20, t79_zfmisc_1, t12_lattice2, t5_funct_2, cc1_yellow13, dt_k8_funct_2, fraenkel_a_2_0_lattice5, t7_closure2, t50_setwiseo, d2_finseq_1, redefinition_k5_setwiseo, t18_setwiseo, d3_zfmisc_1, t72_mcart_1, s9_domain_1, t2_zfmisc_1, t9_altcat_1, fraenkel_a_1_6_domain_1, redefinition_k10_pboole, t167_funct_2, rc6_tex_2, t72_funct_3, t60_zfmisc_1, t24_filter_1, cc1_finseq_1, t24_finset_1, t1_pralg_3, fc1_orders_1, t97_zfmisc_1, redefinition_k7_domain_1, t11_funct_2, t21_funct_5, t28_partfun1, fc2_funct_1, d1_ens_1, t45_enumset1, t73_funct_1, dt_k3_realset1, t40_funct_2, t7_cat_1, fraenkel_a_0_0_domain_1, t4_waybel20, cc1_altcat_1, redefinition_k1_card_fil, t102_zfmisc_1, d2_ens_1, t102_xboole_1, t24_binop_1, t27_funcop_1, t28_relset_1, t24_domain_1, t72_partfun1, t8_funct_1, t51_funcop_1, t121_funct_1, t1_funct_7, existence_m1_orders_3, t9_relat_1, t2_tarski, t56_mcart_1, t23_setwiseo, 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, t54_enumset1, t19_card_3, t122_funct_1, t13_setwiseo, t52_setfam_1, t25_borsuk_1, d1_filter_1, dt_k1_borsuk_1, t74_funct_3, t16_funct_4, t22_sysrel, t61_funcop_1, t114_xboole_1, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t74_funcop_1, d1_funct_4, dt_k1_partfun1, t11_tops_2, t61_funct_4, d2_fraenkel, t76_xboole_1, t71_setwiseo, cc1_funct_2, t32_xboole_1, t14_funct_1, d8_mcart_1, t52_subset_1, t5_ordinal1, t48_enumset1, t4_boole, t36_funct_2, t53_xboole_1, d2_funct_2, cc2_eqrel_1, t84_xboole_1, dt_k9_mcart_1, t23_zfmisc_1, t109_relat_1, t4_cat_1, t57_zfmisc_1, t125_funct_1, t46_funcop_1, d5_realset1, t21_xboole_1, t13_yellow_9, t98_zfmisc_1, t58_subset_1, dt_k11_relset_1, dt_k16_funct_3, dt_k5_metric_1, dt_k4_relat_1, t162_funct_1, t32_domain_1, t43_enumset1, dt_k9_relset_2, rc5_tex_2, t4_subset, dt_k10_cat_2, fc3_xboole_0, t22_ens_1, t29_sysrel, t38_subset_1, t176_orders_1, t16_funcop_1, fraenkel_a_1_3_domain_1, dt_k1_finsub_1, t169_funct_2, t33_sysrel, t29_funcop_1, d14_mcart_1, d2_xboole_0, t30_xboole_1, t99_enumset1, cc1_closure2, dt_k2_funct_1, t81_funct_4, dt_k8_domain_1, t15_realset1, t3_altcat_2, t74_zfmisc_1, t6_cqc_lang, t8_ens_1, t39_subset_1, t72_enumset1, t1_waybel20, t89_funct_3, t8_functor0, t76_relat_1, dt_k1_cat_5, t20_ens_1, d4_tarski, d5_partfun1, t43_funct_1, redefinition_k7_filter_1, dt_k14_funct_3, t141_zfmisc_1, rc2_realset1, t12_zfmisc_1, t26_mcart_1, commutativity_k10_classes2, fc1_qc_lang1, t96_xboole_1, s3_domain_1, t65_funcop_1, t5_filter_2, t80_xboole_1, t20_finsub_1, t58_funct_1, t50_domain_1, t25_finset_1, t88_enumset1, t9_zfmisc_1, t148_funct_2, t79_xboole_1, t106_relat_1, t51_funct_2, reflexivity_r2_zfrefle1, t38_finseq_3, t67_xboole_1, d12_binop_1, t35_setwiseo, fc1_rfinseq, reflexivity_r3_zfrefle1, t39_setfam_1, existence_m2_realset1, t61_enumset1, existence_m3_realset1, t119_enumset1, t12_tops_2, redefinition_k6_setwiseo, t10_mcart_1, t56_subset_1, redefinition_k10_relset_1, dt_k3_ens_1, s1_relset_1, redefinition_k14_mcart_1, t8_funct_5, redefinition_k5_setfam_1, s8_domain_1__e1_38__relset_2, t12_ens_1, s6_filter_1, t47_funcop_1, dt_k1_domain_1, t58_zfmisc_1, t41_enumset1, t20_borsuk_1, t21_funct_3, t17_funct_2, t3_grcat_1, t1_xboole_0, t21_finsub_1, t71_funct_4, involutiveness_k4_relat_1, t35_sysrel, d4_partfun1, t29_xboole_1, t50_funct_4, t5_orders_1, t17_finsub_1, t67_funct_4, t13_lattice2, rc5_triang_1, fc1_realset1, dt_k1_urysohn1, t63_classes2, t11_funct_5, t74_mcart_1, t7_realset1, dt_k6_relset_2, t22_relset_2, commutativity_k5_xboole_0, t59_funct_1, t145_finseq_2, t132_funct_2, t139_zfmisc_1, t36_setfam_1, fc4_qc_lang1, t143_relat_1, t77_relat_1, t13_finset_1, rc3_tex_2, t3_ordinal1, t32_lopclset, t6_realset1, t16_lattice2, t64_classes2, fc5_finseq_1, t7_boole, t7_altcat_1, t37_sysrel, t11_card_fil, t41_domain_1, dt_k4_closure2, cc1_funct_1, t51_finseq_2, t4_funct_2, t2_altcat_1, d2_filter_1, t24_funcop_1, t17_funct_5, t27_membered, t95_funct_3, t136_partfun1, rc3_realset1, d3_funcop_1, t111_finseq_2, fc6_finseq_1, s11_funct_2, t86_funct_3, t104_zfmisc_1, t11_binop_1, t42_mcart_1, t86_enumset1, t138_partfun1, t12_funct_7, t28_domain_1, s2_domain_1, dt_k7_mcart_1, t55_zfmisc_1, t42_finseq_3, d10_relat_1, t66_funct_4, t2_qc_lang1, d10_setfam_1, t1_t_0topsp, d2_subset_1, free_g1_metric_1, t66_zfmisc_1, d3_pboole, fc1_subset_1, t33_zfmisc_1, t29_finseq_1, t33_funct_4, fc29_membered, t22_relat_1, redefinition_k6_partfun1, t105_relat_1, redefinition_k3_classes2, d1_setwiseo, t91_funct_3, t48_xboole_1, dt_k6_domain_1, redefinition_m1_cat_5, t157_funct_1, t9_domain_1, fc38_membered, d5_mcart_1, t45_relset_1, t16_mcart_1, dt_k16_domain_1, t8_pua2mss1, dt_k4_urysohn1, fc2_membered, dt_k11_mcart_1, t6_funct_5, t158_funct_2, t74_relat_1, redefinition_k1_domain_1, t21_funct_2, t130_finseq_2, t20_cantor_1, t3_altcat_1, t14_functor0, t23_borsuk_1, t5_setwiseo, dt_k12_binop_2, t66_funcop_1, t16_subset_1, dt_k2_partfun1, dt_m1_card_fil, t26_zfmisc_1, t70_enumset1, t9_ens_1, t69_partfun1, dt_k9_binop_2, t38_relset_1, t65_funct_4, t7_ordinal1, t153_relat_1, rc2_funct_1, t49_partfun1, redefinition_k10_classes2, dt_k31_binop_2, t9_funct_2, t160_relat_1, cc2_setfam_1, reflexivity_r6_pboole, fc10_relat_1, t31_funct_2, rc1_subset_1, t64_funct_1, t149_funct_2, fc1_closure2, fc2_card_fil, t41_sysrel, t81_funcop_1, t187_relat_1, cc4_membered, t48_funct_1, fraenkel_a_0_0_group_5, t6_fraenkel, t49_relset_1, redefinition_k2_monoid_0, t7_relset_2, t54_setfam_1, t17_ens_1, t47_funct_1, d11_relat_1, fc1_yellow_3, t31_xboole_1, t1_functor1, t63_zfmisc_1, dt_k6_funcop_1, t4_subset_1, t88_xboole_1, t19_funct_2, t18_funct_4, fc1_partfun1, fc4_card_3, t51_funct_1, t26_filter_1, t13_borsuk_1, t8_fraenkel, t30_funct_4, fraenkel_a_3_0_domain_1, t85_xboole_1, t103_finseq_3, t7_funct_5, t22_finset_1, t67_funct_1, t8_lattice2, t90_funct_3, t42_funct_4, t30_relset_1, redefinition_k3_cat_5, t14_zfmisc_1, rc1_funct_2, t91_orders_1, t24_xboole_1, d7_realset1, dt_k10_funct_3, t76_funcop_1, d6_ens_1, t70_funct_4, t56_funct_1, t110_relat_1, t113_funct_2, t71_partfun1, t46_enumset1, fc8_finseq_1, dt_m1_pboole, t69_xboole_1, d5_funct_2, t17_fraenkel, t27_sysrel, t12_setwiseo, cc1_triang_1, d4_realset1, t59_funct_4, existence_m3_pboole, t94_finseq_2, t4_realset1, t11_fraenkel, t159_funct_2, t116_zfmisc_1, redefinition_k13_domain_1, t64_zfmisc_1, d7_xboole_0, fc5_relat_1, t83_xboole_1, d6_setwiseo, t151_relat_1, redefinition_k7_classes2, t1_zfrefle1, t51_setfam_1, t4_borsuk_1, dt_m1_fraenkel, t45_relat_1, dt_m2_finseq_1, t2_lattice2, redefinition_k23_qc_lang1, d8_card_fil, t17_relset_2, t7_card_fil, t5_altcat_2, d1_tex_2, t4_ens_1, t14_funct_2, fc2_funct_7, t155_funct_2, t77_funct_4, t20_xboole_1, t178_orders_1, s2_subset_1, t6_tex_2, t12_funct_3, t50_mcart_1, commutativity_k3_setfam_1, t97_relat_1, d3_funct_4, t16_zfmisc_1, t17_cantor_1, t90_enumset1, t101_zfmisc_1, t4_isocat_2, d3_funct_2, t17_borsuk_1, t2_t_0topsp, redefinition_k8_domain_1, t65_funct_1, d2_funct_5, t134_pboole, t124_zfmisc_1, t188_relat_1, s10_funct_2, d9_binop_2, fraenkel_a_3_1_domain_1, t35_funct_4, t60_funct_2, d16_mcart_1, t82_xboole_1, existence_m1_pboole, t6_setwiseo, dt_k8_vectsp_2, t78_finseq_2, t4_filter_2, t107_relat_1, dt_k2_monoid_0, t32_zfmisc_1, t54_xboole_1, t186_relat_1, t46_setfam_1, t23_funct_4, t55_xboole_1, t3_multop_1, t56_funcop_1, d7_relat_1, t89_relat_1, t10_ens_1, cc2_funct_1, t120_zfmisc_1, t9_relset_2, t169_partfun1, t3_funct_3, t18_funct_1, redefinition_k1_cat_2, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, t16_card_fil, dt_k4_funct_2, t31_subset_1, t2_filter_2, t3_subset, cc1_relset_1, cc1_eqrel_1, t22_relset_1, commutativity_k9_binop_2, t25_binop_1, t98_enumset1, s1_subset_1, t1_cantor_1, d2_binop_1, s1_domain_1, t31_sysrel, t78_relat_1, s4_funct_2, t8_mssubfam, t10_funct_5, t7_pua2mss1, t76_funct_1, t124_funct_1, fraenkel_a_3_1_pua2mss1, dt_k1_cantor_1, dt_k9_cat_2, t55_subset_1, t79_funct_2, t70_mcart_1, dt_k6_funct_3, t46_funct_1, t51_setwiseo, idempotence_k1_funct_4, dt_k6_setfam_1, d15_mcart_1, free_g3_quantal1, t44_setwiseo, t136_funct_2, t6_borsuk_1, fraenkel_a_2_1_domain_1, t14_relset_2, commutativity_k7_subset_1, d2_zfmisc_1, dt_k13_mcart_1, fc11_relat_1, t127_partfun1, t10_altcat_1, existence_m1_subset_1, fc5_subset_1, t1_waybel18, d2_mcart_1, t111_enumset1, d8_binop_2, t41_funct_4, t110_enumset1, commutativity_k2_tarski, t3_relat_1, t13_finseq_2, t26_funct_7, t24_relat_1, t14_funct_7, t8_relset_1, t68_funct_4, d6_xboole_0, t44_zfmisc_1, t14_finsub_1, redefinition_r6_pboole, redefinition_k5_domain_1, t17_relset_1, dt_k9_setwiseo, t91_enumset1, t25_domain_1, t35_xboole_1, t49_domain_1, fc3_yellow_3, t118_enumset1, t7_functor0, t106_zfmisc_1, dt_k11_setwiseo, t12_cantor_1, fraenkel_a_6_0_domain_1, t7_funct_7, fc2_qc_lang1, t16_relset_2, d5_card_3, t125_zfmisc_1, t73_funct_2, t30_subset_1, t8_setwiseo, d17_binop_1, t10_cqc_lang, t54_mcart_1, dt_k2_funct_2, fc3_qc_lang1, t84_funcop_1, commutativity_k5_classes2, dt_k7_relat_1, redefinition_k4_subset_1, t1_monoid_0, rc4_tex_2, t14_xboole_1, t44_setfam_1, t11_relset_1, t5_funct_5, t11_funct_4, rc5_orders_3, t155_relat_1, d8_relat_1, t2_pre_circ, t47_xboole_1, t109_enumset1, t19_numbers, t61_funct_1, commutativity_k8_classes2, d2_card_fil, fc1_finset_1, t15_subset_1, t99_funct_3, t5_grcat_1, t5_lattice2, free_g2_struct_0, t37_funct_2, t94_relat_1, t48_setfam_1, t5_isocat_2, t39_sysrel, t31_funcop_1, t118_funct_1, t132_zfmisc_1, t18_borsuk_1, d5_subset_1, t2_altcat_2, redefinition_k16_funct_3, t29_zfmisc_1, t9_zfrefle1, t146_relat_1, t92_zfmisc_1, redefinition_k4_setwiseo, t99_partfun1, t54_setwiseo, t107_zfmisc_1, redefinition_k2_classes2, t9_realset1, t9_funct_5, existence_m2_subset_1, t95_relat_1, d8_setfam_1, t100_zfmisc_1, t22_zfmisc_1, redefinition_k1_relset_2, redefinition_r2_subset_1, dt_k5_subset_1, dt_k9_funcop_1, t3_funct_7, t64_funct_4, t19_funct_5, t94_enumset1, t8_cantor_1, t64_setwiseo, t121_funct_2, t114_zfmisc_1, cc5_tex_2, fc3_urysohn1, t31_zfmisc_1, t70_funct_1, cc4_tex_2, s4_altcat_1, t58_partfun1, t60_setwiseo, redefinition_k7_pboole, t81_funct_3, t2_multop_1, d1_zfmisc_1, t16_xboole_1, free_g2_vectsp_1, t19_funcop_1, t106_finseq_3, t3_zfrefle1, t1_ens_1, t69_enumset1, t26_xboole_1, t69_mcart_1, t90_finseq_2, s24_fraenkel, t63_xboole_1, redefinition_k7_funcop_1, t26_domain_1, t7_tex_2, t15_xboole_1, t27_funct_4, redefinition_k8_waybel_5, t144_finseq_2, t57_setfam_1, t8_funct_4, t43_funct_2, commutativity_k4_subset_1, fraenkel_a_4_1_relset_2, t125_enumset1, dt_k1_nattra_1, t96_finseq_2, t86_zfmisc_1, rc2_relat_1, existence_m2_relset_1, t98_xboole_1, t16_membered, t2_tex_2, d4_binop_1, t49_funcop_1, t54_domain_1, t38_zfmisc_1, t14_ens_1, t63_funct_4, dt_k13_ens_1, dt_k12_finseq_1, rc1_pua2mss1, t7_ens_1, redefinition_k7_subset_1, t15_cantor_1, t65_mcart_1, t16_ens_1, t4_funct_7, t34_funcop_1, t55_setwiseo, t31_yellow18, d8_ens_1, dt_k3_pre_circ, t37_mcart_1, t73_enumset1, d5_enumset1, t116_funct_2, d12_ens_1, fraenkel_a_3_6_domain_1, t9_functor0, t17_finseq_1, t73_partfun1, redefinition_k3_cantor_1, dt_k7_funcop_1, fc4_funcop_1, t6_funct_2, t69_funcop_1, fraenkel_a_1_0_pua2mss1, t28_finseq_2, t61_card_3, t72_funct_1, s4_domain_1, d14_ens_1, t168_partfun1, t1_isocat_1, t157_relat_1, cc3_finsub_1, t82_funct_3, s14_funct_2, redefinition_k4_domain_1, t62_setwiseo, t26_subset_1, redefinition_k2_binop_1, t6_grcat_1, existence_m2_filter_1, t51_subset_1, t21_subset_1, t111_xboole_1, rc1_triang_1, dt_k4_multop_1, t61_domain_1, t15_funct_3, t15_card_fil, involutiveness_k7_setfam_1, t22_xboole_1, t2_funct_3, t5_pua2mss1, involutiveness_k10_funcop_1, t64_enumset1, t84_zfmisc_1, t13_funct_5, t76_enumset1, t67_classes2, t27_borsuk_1, t62_funct_4, t113_enumset1, t40_sysrel, reflexivity_r1_filter_2, t3_pua2mss1, t8_setfam_1, t36_zfmisc_1, d4_classes2, d8_monoid_0, d7_monoid_0, t41_subset_1, t26_membered, redefinition_k5_funct_4, dt_k12_mcart_1, redefinition_k6_funcop_1, redefinition_k17_domain_1, t14_setwiseo, t73_finseq_1, t20_card_3, t100_xboole_1, t84_funct_3, t8_xboole_1, t8_realset1, t103_xboole_1, t25_ens_1, t58_funcop_1, t37_relat_1, rc2_cat_5, t6_relset_1, t78_xboole_1, t28_xboole_1, t16_borsuk_1, d1_relset_1, d3_tarski, d6_card_fil, t74_partfun1, t31_filter_1, t53_domain_1, d1_funct_3, t58_enumset1, d1_multop_1, t46_subset_1, t151_pboole, t18_binop_1, redefinition_k16_domain_1, cc6_funct_2, t74_funct_4, t43_funcop_1, dt_k8_binop_2, dt_k15_classes2, t76_funct_4, t33_domain_1, t60_subset_1, t39_zfmisc_1, d1_realset1, t15_funct_7, t19_functor0, t58_funct_4, t72_setwiseo, t131_funct_2, t119_zfmisc_1, dt_k7_pboole, t5_xboole_0, d8_realset1, d7_card_fil, redefinition_k1_cat_5, rc1_relat_1, t34_mcart_1, t13_xboole_1, t60_relat_1, t54_funct_1, t13_cantor_1, t42_funcop_1, t19_setwiseo, t83_zfmisc_1, t80_finseq_2, t40_subset_1, t2_monoid_0, t54_zfmisc_1, t13_card_fil, fraenkel_a_3_4_domain_1, s22_fraenkel, dt_k5_relat_1, t17_subset_1, t57_setwiseo, dt_k4_qc_lang1, t148_relat_1, reflexivity_r1_tarski, t9_funct_1, t6_orders_1, fraenkel_a_0_0_card_fil, symmetry_r2_subset_1, dt_k6_relat_1, t143_funct_2, t70_funct_3, fc2_urysohn1, t20_finset_1, t32_setwiseo, cc17_membered, t6_zfmisc_1, dt_k14_borsuk_1, t41_finseq_2, t1_mssubfam, t48_relat_1, dt_k10_relset_1, symmetry_r1_filter_2, d2_orders_1, t27_finsub_1, s3_subset_1, t5_mcart_1, t93_relat_1, t33_borsuk_1, t18_funct_2, redefinition_k1_classes2, dt_k4_relset_2, t121_zfmisc_1, t10_subset_1, t161_relat_1, dt_k7_filter_1, t19_ens_1, t51_funct_4, t139_finseq_2, t56_setfam_1, redefinition_k1_partfun1, rc2_setwiseo, t17_card_fil, t1_realset1, t7_cqc_lang, t36_setwiseo, t53_enumset1, reflexivity_r4_nattra_1, t2_xboole_1, t4_xboole_1, t57_partfun1, t141_partfun1, d12_funct_1, t9_relset_1, redefinition_k2_realset1, t17_funct_4, fc2_yellow_3, dt_k5_classes2, t9_mcart_1, t7_msualg_1, t11_funcop_1, dt_k5_funct_4, t34_setfam_1, t37_funcop_1, fraenkel_a_0_38_fraenkel, t59_zfmisc_1, fc6_relat_1, dt_k4_domain_1, free_g2_rlvect_1, s1_card_fil, t51_domain_1, t1_partfun1, existence_m4_realset1, t41_xboole_1, idempotence_k7_classes2, t79_enumset1, t34_funct_2, t11_funct_7, t83_enumset1, t57_subset_1, t47_zfmisc_1, d15_binop_1, t1_latsum_1, d1_funct_2, t12_funct_6, t3_lattice4, dt_k6_setwiseo, t2_setfam_1, t61_mcart_1, t18_zfmisc_1, t6_pua2mss1, t25_funct_4, t20_relat_1, t90_xboole_1, t8_relset_2, t51_relat_1, t2_ens_1, t31_domain_1, free_g3_lattices, redefinition_k11_domain_1, t46_relat_1, fc1_setfam_1, t39_mcart_1, d15_ens_1, d5_functor0, t66_funct_1, t3_card_fil, d1_funct_7, d4_xboole_0, redefinition_v1_yellow18, t7_funct_4, t43_setwiseo, t65_setwiseo, t68_setwiseo, t12_zfrefle1, t35_funct_1, t29_relset_1, rc1_realset1, dt_k11_ens_1, s4_multop_1, redefinition_k7_relset_1, t3_monoid_0, t3_isocat_2, t17_funcop_1, dt_k5_setfam_1, rc3_finset_1, t68_funct_1, t24_ens_1, d6_eqrel_1, dt_k2_nattra_1, dt_k5_setwiseo, existence_m1_eqrel_1, commutativity_k5_setwiseo, dt_k1_metric_1, t30_finseq_2, t45_partfun1, s2_pua2mss1, t36_xboole_1, t51_zfmisc_1, redefinition_k14_funct_3, dt_k8_subset_1, rc8_finseq_1, t3_ens_1, t144_partfun1, t20_funct_5, fc12_binop_2, existence_m1_nat_lat, t4_card_fil, t94_xboole_1, t73_zfmisc_1, t47_subset_1, redefinition_k4_multop_1, t123_partfun1, t151_funct_2, dt_k12_domain_1, t46_relset_1, t47_funct_4, t64_xboole_1, t49_xboole_1, dt_k1_cat_1, t64_mcart_1, t71_mcart_1, d5_binop_1, dt_m2_subset_1, dt_k5_numbers, t51_relset_1, dt_k8_setwiseo, dt_k6_ens_1, redefinition_k1_finsub_1, t19_borsuk_1, t18_yellow_9, t12_funct_2, d16_binop_1, t54_subset_1, t53_funct_1, t27_finseq_1, rc1_finset_1, dt_k7_setfam_1, t28_finsub_1, t127_zfmisc_1, d1_cat_1, t10_fraenkel, t123_funct_1, redefinition_k2_functor0, dt_k2_yellow_3, t70_funcop_1, t40_funct_4, t11_setfam_1, t50_relset_1, t44_subset_1, t87_relat_1, cc1_finset_1, commutativity_k11_binop_2, t14_mcart_1, t35_partfun1, d1_yellow18, d8_binop_1, t93_xboole_1, t5_cqc_lang, t21_funct_1, t50_funct_1, fc12_finset_1, t87_enumset1, t42_funct_1, t26_finsub_1, t8_card_fil, t73_mcart_1, t2_nattra_1, fc1_relat_1, d3_setwiseo, d10_binop_2, t4_mssubfam, t77_xboole_1, t10_setfam_1, cc6_membered, t8_boole, rc1_xboole_0, existence_m1_fraenkel, t108_finseq_3, fc1_waybel_2, t21_borsuk_1, t18_sysrel, t16_funct_3, t1_funct_5, t1_mcart_1, t103_enumset1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, t35_mcart_1, t35_relset_1, d1_orders_1, t16_sysrel, d9_card_fil, dt_m2_finseq_2, t80_zfmisc_1, t18_card_3, t34_zfmisc_1, t18_functor0, fc3_funct_1, t6_functor0, t6_multop_1, t102_enumset1, t16_finseq_2, t60_enumset1, t26_setwiseo, t5_relat_1, t24_zfmisc_1, t68_zfmisc_1, rc2_tex_2, t22_membered, dt_k36_binop_2, dt_k6_mcart_1, rc7_tex_2, t1_functor0, t23_relat_1, dt_k7_metric_1, dt_m1_orders_1, dt_k12_funct_3, t54_funcop_1, t120_funct_2, d1_borsuk_1, t31_mcart_1, t67_mcart_1, t46_funct_4, involutiveness_k7_binop_2, redefinition_k9_relset_2, t59_funct_2, dt_k33_binop_2, t12_xboole_1, t22_funct_3, t10_zfmisc_1, t56_classes2, t2_subset, existence_m1_finseq_2, s1_binop_2, t100_funct_3, t20_sysrel, reflexivity_r1_partfun1, t38_funct_2, t33_partfun1, rc1_closure2, t34_finsub_1, d3_relat_1, t85_funct_2, fc1_tex_2, t45_domain_1, t12_altcat_1, t46_yellow20, t16_finset_1, t42_domain_1, dt_k6_classes2, d2_multop_1, fc2_yellow21, dt_k2_multop_1, t75_funcop_1, fc7_relat_1, t14_funcop_1, t4_qc_lang1, t47_mcart_1, s1_pre_circ, commutativity_k4_finsub_1, t60_funct_1, t111_relat_1, d11_ens_1, dt_k3_cat_5, dt_k8_mcart_1, t21_yellow_9, t24_funct_4, t11_functor0, fc2_relat_1, t14_finseq_1, t37_zfmisc_1, t52_setwiseo, t65_relat_1, t21_relat_1, t3_pboole, t156_relat_1, dt_k10_classes2, t23_finsub_1, t53_zfmisc_1, t30_finsub_1, fc1_funct_7, dt_k23_qc_lang1, t14_borsuk_1, d4_setwiseo, d4_mcart_1, t15_finseq_2, t109_zfmisc_1, redefinition_k6_cqc_lang, d10_lattice5, fraenkel_a_2_3_domain_1, t60_domain_1, t117_enumset1, t25_finsub_1, d1_setfam_1, t152_relat_1, symmetry_r1_xboole_0, t49_funct_4, t134_zfmisc_1, t86_relat_1, t28_finset_1, free_g1_rlvect_1, dt_k5_mcart_1, t100_relat_1, t78_mcart_1, t25_partfun1, t49_relat_1, d12_binop_2, t126_zfmisc_1, t12_domain_1, fraenkel_a_3_1_card_fil, rc3_closure2, dt_k2_cantor_1, t13_finsub_1, fc8_relat_1, t27_funct_1, t10_realset1, t92_relat_1, d11_binop_2, t82_funcop_1, redefinition_k2_cat_5, dt_k10_mcart_1, t175_orders_1, s10_fraenkel, dt_k3_binop_1, t15_functor0, t40_relat_1, fraenkel_a_0_18_fraenkel, t40_finseq_3, idempotence_k8_classes2, t75_mcart_1, fc2_funcop_1, t59_enumset1, fraenkel_a_2_1_card_fil, dt_k10_ens_1, t55_enumset1, t58_domain_1, t115_funct_2, free_g1_quantal1, t4_waybel18, idempotence_k2_xboole_0, t13_mcart_1, t48_funct_4, dt_k12_classes2, t32_finsub_1, t48_subset_1, t129_finseq_2, rc1_setwiseo, d18_pboole, dt_k1_pcomps_1, t28_relat_1, t17_mcart_1, d1_funct_1, d1_filter_2, t32_borsuk_1, t31_finseq_2, t1_pralg_1, t44_funct_4, dt_k1_relset_2, fc2_ens_1, redefinition_k5_funcsdom, redefinition_k2_funct_3, redefinition_k10_cat_2, t145_relat_1, t50_subset_1, t1_nattra_1, t11_relset_2, t46_xboole_1, t107_xboole_1, d10_xboole_0, t1_tex_2, t27_filter_1, t149_relat_1, d3_pua2mss1, d11_setfam_1, dt_k2_qc_lang1, fc2_realset1, t2_lattice5, t74_xboole_1, fc2_finset_1, fraenkel_a_1_0_ens_1, fraenkel_a_0_33_fraenkel, redefinition_k18_group_2, redefinition_k10_domain_1, t7_xboole_1, t10_relset_2, t8_funct_7, t2_grcat_1, t37_funct_1, t59_classes2, t3_xboole_0, t67_partfun1, fc2_fraenkel, cc1_realset1, t58_setfam_1, t12_relset_1, t77_funcop_1, d2_funct_4, dt_k18_group_2, fc3_funcop_1, t5_xboole_1, fc4_binop_2, t49_subset_1, fc1_funcop_1, t44_funcop_1, t7_tarski, t15_borsuk_1, t108_relat_1, t33_funct_1, t145_funct_2, t141_funct_2, t43_mcart_1, t3_setwiseo, rc1_partfun1, redefinition_r1_filter_2, t40_ens_1, t28_setwiseo, redefinition_m1_pua2mss1, dt_k3_funct_4, redefinition_k5_relset_1, rc1_card_fil, redefinition_k2_nattra_1, t57_funct_1, t120_partfun1, fraenkel_a_3_0_ens_1, t27_partfun1, symmetry_r1_partfun1, d5_ens_1, t2_funct_7, t91_xboole_1, dt_k2_setwiseo, t23_filter_1, t3_boole, redefinition_k2_setwiseo, d8_funct_3, d9_funct_3, d5_funct_1, t48_mcart_1, t6_ordinal1, t53_mcart_1, t146_finseq_2, dt_k10_pboole, fc1_ens_1, redefinition_k6_subset_1, t93_zfmisc_1, dt_k2_funct_3, t140_finseq_2, redefinition_k4_relset_1, t44_funct_1, t10_finsub_1, cc5_funct_2, t48_relset_1, t57_sysrel, redefinition_m2_subset_1, t69_setwiseo, d4_enumset1, redefinition_k1_borsuk_1, t87_funct_3, t59_funcop_1, t25_relat_1, t22_funct_2, t62_finseq_3, t99_xboole_1, t4_pralg_1, t16_domain_1, fc1_sysrel, t5_funct_4, fc16_finset_1, t13_binop_1, dt_k34_binop_2, t83_funct_3, dt_k1_oppcat_1, d5_setwiseo, fc1_yellow21, t87_xboole_1, t67_funct_2, t26_partfun1, redefinition_k2_partfun1, fc14_finset_1, dt_k15_funct_3, t8_multop_1, fc4_realset1, t11_ens_1, t17_funct_3, t78_enumset1, t26_funct_4, t40_mcart_1, rc1_tex_2, t36_relset_1, t103_relat_1, dt_k5_finsub_1, t30_zfmisc_1, s2_multop_1, dt_k10_domain_1, t80_relat_1, cc16_membered, t15_sysrel, fraenkel_a_0_1_domain_1, t16_binop_1, fc13_finset_1, redefinition_k6_classes2, rc1_setfam_1, t45_mcart_1, t15_funct_4, t139_partfun1, dt_k2_zfrefle1, d13_binop_1, t9_card_fil, fc7_finset_1, idempotence_k4_subset_1, t21_closure2, t34_setwiseo, d5_finsub_1, symmetry_r6_pboole, t26_sysrel, dt_k7_cat_1, t143_partfun1, d2_setwiseo, fraenkel_a_0_39_fraenkel, d10_ens_1, dt_k13_funct_3, d1_binop_1, t71_enumset1, t81_relat_1, t40_zfmisc_1, t72_funcop_1, t82_mcart_1, t22_funct_4, fc22_membered, rc2_xboole_0, dt_k3_card_fil, t174_partfun1, t55_funct_2, fraenkel_a_3_5_domain_1, t82_funct_4, redefinition_r4_nattra_1, t45_xboole_1, t66_relat_1, t38_partfun1, fc27_membered, existence_m1_card_fil, s7_domain_1, d3_monoid_0, t141_finseq_2, existence_m1_orders_1, symmetry_r2_zfrefle1, t112_zfmisc_1, t8_funct_3, t40_xboole_1, dt_m3_realset1, t5_closure2, t2_xboole_0, redefinition_k4_finseq_1, redefinition_k12_classes2, d3_xboole_0, d2_relat_1, d4_funcop_1, t71_relat_1, irreflexivity_r2_subset_1, t61_funct_2, t52_mcart_1, t36_funct_4, t62_domain_1, t10_xboole_1, redefinition_k12_domain_1, d3_binop_1, t28_funct_2, dt_k3_subset_1, fraenkel_a_0_2_domain_1, d2_relset_2, fc1_funct_2, existence_m2_finseq_1, t2_funct_4, fc23_membered, t147_finseq_2, t125_partfun1, t38_setwiseo, t96_enumset1, t66_classes2, cc1_binop_1, t6_relat_1, rc1_finseq_2, dt_k17_monoid_0, s18_fraenkel, t172_partfun1, t33_subset_1, t2_waybel18, t14_lattice2, t31_borsuk_1, t15_ens_1, t159_relat_1, dt_k3_qc_lang1, t10_card_fil, t32_funct_4, fraenkel_a_3_8_domain_1, t6_yellow21, t65_zfmisc_1, t30_partfun1, t80_funct_4, dt_k3_classes2, cc6_tex_2, t63_enumset1, redefinition_k9_funcop_1, t63_subset_1, t112_partfun1, fraenkel_a_4_1_domain_1, t38_xboole_1, t19_funct_4, redefinition_k9_cat_2, t39_xboole_1, redefinition_k8_setwiseo, t43_cqc_lang, t23_funcop_1, d7_binop_2, t20_funct_4, antisymmetry_r2_hidden, t23_relset_1, t15_relset_2, t88_funct_3, d1_mcart_1, dt_k1_setwiseo, t53_setfam_1, fc15_finset_1, t45_funct_4, t88_relat_1, redefinition_k15_domain_1, t26_relat_1, t42_enumset1, t18_mcart_1, t53_relat_1, fc3_binop_2, t21_lattice5, t22_subset_1, redefinition_k6_domain_1
% 109.28/54.86 % No. of inferences in proof: 5190
% 109.28/54.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 54356 ms resp. 52291 ms w/o parsing
% 115.68/57.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 115.87/58.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------