TSTP Solution File: TOP024+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : TOP024+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:38:41 EDT 2023
% Result : Theorem 129.91s 33.40s
% Output : Refutation 132.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2502
% Syntax : Number of formulae : 4680 ( 213 unt; 326 typ; 0 def)
% Number of atoms : 30496 (3083 equ; 0 cnn)
% Maximal formula atoms : 43 ( 7 avg)
% Number of connectives : 106864 (5178 ~; 209 |;13762 &;75544 @)
% ( 464 <=>;11707 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 673 ( 673 >; 0 *; 0 +; 0 <<)
% Number of symbols : 328 ( 326 usr; 30 con; 0-8 aty)
% Number of variables : 13165 ( 0 ^;12483 !; 682 ?;13165 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v2_pre_topc_type,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_type,type,
l1_pre_topc: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v1_tsp_2_type,type,
v1_tsp_2: $i > $i > $o ).
thf(v1_tops_1_type,type,
v1_tops_1: $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k16_funct_3_type,type,
k16_funct_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k1_partfun1_type,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k5_numbers_type,type,
k5_numbers: $i ).
thf(k1_numbers_type,type,
k1_numbers: $i ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(r3_binop_1_type,type,
r3_binop_1: $i > $i > $i > $o ).
thf(r2_binop_1_type,type,
r2_binop_1: $i > $i > $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_type,type,
k3_partfun1: $i > $i > $i > $i ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k4_relset_1_type,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k4_relat_1_type,type,
k4_relat_1: $i > $i ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(v4_ordinal2_type,type,
v4_ordinal2: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(r1_binop_1_type,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(v3_relat_2_type,type,
v3_relat_2: $i > $o ).
thf(v8_relat_2_type,type,
v8_relat_2: $i > $o ).
thf(v1_relat_2_type,type,
v1_relat_2: $i > $o ).
thf(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(k12_mcart_1_type,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k10_relat_1_type,type,
k10_relat_1: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k3_funcop_1_type,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k7_eqrel_1_type,type,
k7_eqrel_1: $i > $i > $i ).
thf(k4_funcop_1_type,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(k6_eqrel_1_type,type,
k6_eqrel_1: $i > $i > $i > $i ).
thf(r1_partfun1_type,type,
r1_partfun1: $i > $i > $o ).
thf(r5_binop_1_type,type,
r5_binop_1: $i > $i > $i > $o ).
thf(r4_binop_1_type,type,
r4_binop_1: $i > $i > $i > $o ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k10_relset_1_type,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(k6_funcop_1_type,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k2_funcop_1_type,type,
k2_funcop_1: $i > $i > $i ).
thf(v1_setfam_1_type,type,
v1_setfam_1: $i > $o ).
thf(k4_funct_2_type,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k8_eqrel_1_type,type,
k8_eqrel_1: $i > $i > $i ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v3_tops_2_type,type,
v3_tops_2: $i > $i > $i > $o ).
thf(k2_pre_topc_type,type,
k2_pre_topc: $i > $i ).
thf(v4_pre_topc_type,type,
v4_pre_topc: $i > $i > $o ).
thf(k4_pre_topc_type,type,
k4_pre_topc: $i > $i > $i > $i > $i ).
thf(g1_metric_1_type,type,
g1_metric_1: $i > $i > $i ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(v5_pre_topc_type,type,
v5_pre_topc: $i > $i > $i > $o ).
thf(k2_tops_2_type,type,
k2_tops_2: $i > $i > $i > $i ).
thf(k5_funcop_1_type,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(k5_relset_1_type,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(v2_tops_1_type,type,
v2_tops_1: $i > $i > $o ).
thf(k1_tops_1_type,type,
k1_tops_1: $i > $i > $i ).
thf(k5_pre_topc_type,type,
k5_pre_topc: $i > $i > $i > $i > $i ).
thf(k5_xboole_0_type,type,
k5_xboole_0: $i > $i > $i ).
thf(k6_pre_topc_type,type,
k6_pre_topc: $i > $i > $i ).
thf(k1_setfam_1_type,type,
k1_setfam_1: $i > $i ).
thf(m1_pre_topc_type,type,
m1_pre_topc: $i > $i > $o ).
thf(r1_tsep_1_type,type,
r1_tsep_1: $i > $i > $i > $o ).
thf(v1_pre_topc_type,type,
v1_pre_topc: $i > $o ).
thf(k2_tsep_1_type,type,
k2_tsep_1: $i > $i > $i > $i ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(k1_tsep_1_type,type,
k1_tsep_1: $i > $i > $i > $i ).
thf(k1_pre_topc_type,type,
k1_pre_topc: $i > $i ).
thf(v3_pre_topc_type,type,
v3_pre_topc: $i > $i > $o ).
thf(v4_tex_3_type,type,
v4_tex_3: $i > $i > $o ).
thf(m2_subset_1_type,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k2_borsuk_1_type,type,
k2_borsuk_1: $i > $i > $i ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k11_relset_1_type,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(l2_struct_0_type,type,
l2_struct_0: $i > $o ).
thf(v2_struct_0_type,type,
v2_struct_0: $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(v3_tdlat_3_type,type,
v3_tdlat_3: $i > $o ).
thf(v4_tdlat_3_type,type,
v4_tdlat_3: $i > $o ).
thf(v5_tdlat_3_type,type,
v5_tdlat_3: $i > $o ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(k8_funcop_1_type,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k7_funcop_1_type,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k1_funct_3_type,type,
k1_funct_3: $i > $i ).
thf(k9_funct_3_type,type,
k9_funct_3: $i > $i > $i ).
thf(k1_t_0topsp_type,type,
k1_t_0topsp: $i > $i ).
thf(v1_realset1_type,type,
v1_realset1: $i > $o ).
thf(v1_tex_2_type,type,
v1_tex_2: $i > $i > $o ).
thf(r1_pcomps_1_type,type,
r1_pcomps_1: $i > $i > $o ).
thf(k6_pcomps_1_type,type,
k6_pcomps_1: $i > $i > $i ).
thf(l1_metric_1_type,type,
l1_metric_1: $i > $o ).
thf(k5_pcomps_1_type,type,
k5_pcomps_1: $i > $i ).
thf(v3_tex_3_type,type,
v3_tex_3: $i > $i > $o ).
thf(k3_tex_4_type,type,
k3_tex_4: $i > $i > $i ).
thf(u1_metric_1_type,type,
u1_metric_1: $i > $i ).
thf(v3_tops_1_type,type,
v3_tops_1: $i > $i > $o ).
thf(v2_t_0topsp_type,type,
v2_t_0topsp: $i > $o ).
thf(m2_tsp_1_type,type,
m2_tsp_1: $i > $i > $o ).
thf(k7_relset_1_type,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v1_borsuk_1_type,type,
v1_borsuk_1: $i > $i > $o ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(r3_tsep_1_type,type,
r3_tsep_1: $i > $i > $i > $o ).
thf(k9_funcop_1_type,type,
k9_funcop_1: $i > $i > $i > $i > $i ).
thf(k10_funct_3_type,type,
k10_funct_3: $i > $i > $i ).
thf(r4_tsep_1_type,type,
r4_tsep_1: $i > $i > $i > $o ).
thf(k10_funcop_1_type,type,
k10_funcop_1: $i > $i > $i > $i > $i ).
thf(r7_binop_1_type,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k1_tops_2_type,type,
k1_tops_2: $i > $i > $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(v1_tsep_1_type,type,
v1_tsep_1: $i > $i > $o ).
thf(k3_binop_1_type,type,
k3_binop_1: $i > $i > $i ).
thf(k1_enumset1_type,type,
k1_enumset1: $i > $i > $i > $i ).
thf(v1_tdlat_3_type,type,
v1_tdlat_3: $i > $o ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(k6_borsuk_1_type,type,
k6_borsuk_1: $i > $i > $i ).
thf(k1_pcomps_1_type,type,
k1_pcomps_1: $i > $i ).
thf(k12_borsuk_1_type,type,
k12_borsuk_1: $i > $i > $i ).
thf(k13_borsuk_1_type,type,
k13_borsuk_1: $i > $i > $i ).
thf(m1_borsuk_1_type,type,
m1_borsuk_1: $i > $i > $o ).
thf(v2_borsuk_1_type,type,
v2_borsuk_1: $i > $i > $o ).
thf(g1_pre_topc_type,type,
g1_pre_topc: $i > $i > $i ).
thf(u1_pre_topc_type,type,
u1_pre_topc: $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(v2_tex_2_type,type,
v2_tex_2: $i > $i > $o ).
thf(v1_tex_3_type,type,
v1_tex_3: $i > $i > $o ).
thf(v2_tex_3_type,type,
v2_tex_3: $i > $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(k7_tex_4_type,type,
k7_tex_4: $i > $i > $i ).
thf(g2_struct_0_type,type,
g2_struct_0: $i > $i > $i ).
thf(k3_pre_topc_type,type,
k3_pre_topc: $i > $i > $i ).
thf(k18_borsuk_1_type,type,
k18_borsuk_1: $i > $i > $i > $i ).
thf(k3_funct_3_type,type,
k3_funct_3: $i > $i ).
thf(r2_tsep_1_type,type,
r2_tsep_1: $i > $i > $i > $o ).
thf(k16_borsuk_1_type,type,
k16_borsuk_1: $i > $i > $i ).
thf(r4_tsep_2_type,type,
r4_tsep_2: $i > $i > $i > $o ).
thf(r1_connsp_1_type,type,
r1_connsp_1: $i > $i > $i > $o ).
thf(v5_tex_2_type,type,
v5_tex_2: $i > $i > $o ).
thf(k1_tex_2_type,type,
k1_tex_2: $i > $i > $i ).
thf(v2_tdlat_3_type,type,
v2_tdlat_3: $i > $o ).
thf(v1_tex_4_type,type,
v1_tex_4: $i > $i > $o ).
thf(v4_tex_4_type,type,
v4_tex_4: $i > $i > $o ).
thf(k5_tex_4_type,type,
k5_tex_4: $i > $i > $i ).
thf(k4_tex_4_type,type,
k4_tex_4: $i > $i > $i ).
thf(k1_struct_0_type,type,
k1_struct_0: $i > $i > $i ).
thf(a_2_9_tex_4_type,type,
a_2_9_tex_4: $i > $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(k7_subset_1_type,type,
k7_subset_1: $i > $i > $i > $i ).
thf(r1_borsuk_1_type,type,
r1_borsuk_1: $i > $i > $o ).
thf(v3_tex_2_type,type,
v3_tex_2: $i > $i > $o ).
thf(k1_borsuk_1_type,type,
k1_borsuk_1: $i > $i > $i > $i ).
thf(a_3_0_borsuk_1_type,type,
a_3_0_borsuk_1: $i > $i > $i > $i ).
thf(u2_struct_0_type,type,
u2_struct_0: $i > $i ).
thf(m1_connsp_2_type,type,
m1_connsp_2: $i > $i > $i > $o ).
thf(v5_compts_1_type,type,
v5_compts_1: $i > $o ).
thf(v2_tsp_2_type,type,
v2_tsp_2: $i > $i > $o ).
thf(k1_tsp_2_type,type,
k1_tsp_2: $i > $i > $i ).
thf(k21_borsuk_1_type,type,
k21_borsuk_1: $i > $i > $i > $i ).
thf(k20_borsuk_1_type,type,
k20_borsuk_1: $i > $i > $i > $i ).
thf(k2_tops_1_type,type,
k2_tops_1: $i > $i > $i ).
thf(v3_borsuk_1_type,type,
v3_borsuk_1: $i > $i > $i > $o ).
thf(v2_tsp_1_type,type,
v2_tsp_1: $i > $i > $o ).
thf(k2_funct_3_type,type,
k2_funct_3: $i > $i > $i > $i ).
thf(k4_tsp_2_type,type,
k4_tsp_2: $i > $i > $i ).
thf(m2_connsp_2_type,type,
m2_connsp_2: $i > $i > $i > $o ).
thf(k7_setfam_1_type,type,
k7_setfam_1: $i > $i > $i ).
thf(k4_pcomps_1_type,type,
k4_pcomps_1: $i > $i ).
thf(v1_tops_2_type,type,
v1_tops_2: $i > $i > $o ).
thf(k2_t_0topsp_type,type,
k2_t_0topsp: $i > $i ).
thf(k9_funct_2_type,type,
k9_funct_2: $i > $i > $i > $i ).
thf(k7_borsuk_1_type,type,
k7_borsuk_1: $i > $i > $i > $i > $i ).
thf(r3_tsep_2_type,type,
r3_tsep_2: $i > $i > $i > $o ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(k3_t_0topsp_type,type,
k3_t_0topsp: $i > $i ).
thf(k4_t_0topsp_type,type,
k4_t_0topsp: $i > $i ).
thf(k8_borsuk_1_type,type,
k8_borsuk_1: $i > $i > $i > $i > $i ).
thf(k15_borsuk_1_type,type,
k15_borsuk_1: $i > $i ).
thf(k4_borsuk_1_type,type,
k4_borsuk_1: $i > $i > $i > $i > $i > $i ).
thf(k3_borsuk_1_type,type,
k3_borsuk_1: $i > $i > $i > $i ).
thf(r1_subset_1_type,type,
r1_subset_1: $i > $i > $o ).
thf(k17_borsuk_1_type,type,
k17_borsuk_1: $i > $i > $i ).
thf(v3_pcomps_1_type,type,
v3_pcomps_1: $i > $o ).
thf(v1_tops_3_type,type,
v1_tops_3: $i > $i > $o ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(k2_tex_4_type,type,
k2_tex_4: $i > $i > $i ).
thf(k6_tex_4_type,type,
k6_tex_4: $i > $i > $i ).
thf(k2_pcomps_1_type,type,
k2_pcomps_1: $i > $i ).
thf(v1_pcomps_1_type,type,
v1_pcomps_1: $i > $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(a_3_0_pcomps_1_type,type,
a_3_0_pcomps_1: $i > $i > $i > $i ).
thf(a_2_5_tex_4_type,type,
a_2_5_tex_4: $i > $i > $i ).
thf(v2_tops_2_type,type,
v2_tops_2: $i > $i > $o ).
thf(a_2_0_borsuk_1_type,type,
a_2_0_borsuk_1: $i > $i > $i ).
thf(k1_tex_4_type,type,
k1_tex_4: $i > $i > $i ).
thf(k14_borsuk_1_type,type,
k14_borsuk_1: $i > $i > $i > $i > $i ).
thf(r1_pre_topc_type,type,
r1_pre_topc: $i > $i > $o ).
thf(v1_t_0topsp_type,type,
v1_t_0topsp: $i > $i > $i > $o ).
thf(k2_tsp_2_type,type,
k2_tsp_2: $i > $i > $i ).
thf(v3_tsp_1_type,type,
v3_tsp_1: $i > $i > $o ).
thf(f1_s4_funct_2_type,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_type,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_type,type,
f3_s4_funct_2: $i > $i ).
thf(k22_borsuk_1_type,type,
k22_borsuk_1: $i ).
thf(m1_tsp_1_type,type,
m1_tsp_1: $i > $i > $o ).
thf(v5_tops_1_type,type,
v5_tops_1: $i > $i > $o ).
thf(a_2_4_tex_4_type,type,
a_2_4_tex_4: $i > $i > $i ).
thf(v4_tops_1_type,type,
v4_tops_1: $i > $i > $o ).
thf(k19_borsuk_1_type,type,
k19_borsuk_1: $i > $i > $i > $i ).
thf(r1_connsp_2_type,type,
r1_connsp_2: $i > $i > $o ).
thf(k1_connsp_1_type,type,
k1_connsp_1: $i > $i > $i ).
thf(k5_borsuk_1_type,type,
k5_borsuk_1: $i > $i > $i > $i > $i > $i ).
thf(k3_tsp_2_type,type,
k3_tsp_2: $i > $i > $i ).
thf(f1_s14_funct_2_type,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_type,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_type,type,
p1_s14_funct_2: $i > $i > $o ).
thf(a_2_1_borsuk_1_type,type,
a_2_1_borsuk_1: $i > $i > $i ).
thf(f1_s13_funct_2_type,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_type,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_type,type,
f2_s13_funct_2: $i ).
thf(a_2_2_borsuk_1_type,type,
a_2_2_borsuk_1: $i > $i > $i ).
thf(f1_s12_funct_2_type,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_type,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_type,type,
f2_s12_funct_2: $i ).
thf(v2_pcomps_1_type,type,
v2_pcomps_1: $i > $o ).
thf(a_2_3_borsuk_1_type,type,
a_2_3_borsuk_1: $i > $i > $i ).
thf(r2_borsuk_1_type,type,
r2_borsuk_1: $i > $i > $o ).
thf(v6_tops_1_type,type,
v6_tops_1: $i > $i > $o ).
thf(v1_connsp_2_type,type,
v1_connsp_2: $i > $o ).
thf(v2_connsp_1_type,type,
v2_connsp_1: $i > $i > $o ).
thf(v1_tsp_1_type,type,
v1_tsp_1: $i > $i > $o ).
thf(v6_compts_1_type,type,
v6_compts_1: $i > $i > $o ).
thf(k10_borsuk_1_type,type,
k10_borsuk_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k3_metric_1_type,type,
k3_metric_1: $i ).
thf(v2_compts_1_type,type,
v2_compts_1: $i > $o ).
thf(k23_borsuk_1_type,type,
k23_borsuk_1: $i ).
thf(k24_borsuk_1_type,type,
k24_borsuk_1: $i ).
thf(v4_tex_2_type,type,
v4_tex_2: $i > $i > $o ).
thf(f1_s3_funct_2_type,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_type,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_type,type,
p1_s3_funct_2: $i > $i > $o ).
thf(a_3_1_borsuk_1_type,type,
a_3_1_borsuk_1: $i > $i > $i > $i ).
thf(k11_borsuk_1_type,type,
k11_borsuk_1: $i > $i > $i > $i ).
thf(r2_connsp_2_type,type,
r2_connsp_2: $i > $i > $i > $o ).
thf(v3_compts_1_type,type,
v3_compts_1: $i > $o ).
thf(a_1_0_t_0topsp_type,type,
a_1_0_t_0topsp: $i > $i ).
thf(k3_pcomps_1_type,type,
k3_pcomps_1: $i > $i > $i ).
thf(k1_connsp_2_type,type,
k1_connsp_2: $i > $i > $i ).
thf(k2_struct_0_type,type,
k2_struct_0: $i > $i > $i > $i ).
thf(r2_tsep_2_type,type,
r2_tsep_2: $i > $i > $i > $o ).
thf(f3_s11_funct_2_type,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_type,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_type,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_type,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_type,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_type,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_type,type,
f7_s11_funct_2: $i > $i ).
thf(r1_setfam_1_type,type,
r1_setfam_1: $i > $i > $o ).
thf(a_2_7_tex_4_type,type,
a_2_7_tex_4: $i > $i > $i ).
thf(a_3_1_pcomps_1_type,type,
a_3_1_pcomps_1: $i > $i > $i > $i ).
thf(v3_tex_4_type,type,
v3_tex_4: $i > $i > $o ).
thf(a_2_2_tex_4_type,type,
a_2_2_tex_4: $i > $i > $i ).
thf(r3_connsp_1_type,type,
r3_connsp_1: $i > $i > $o ).
thf(k9_borsuk_1_type,type,
k9_borsuk_1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s3_subset_1_type,type,
f1_s3_subset_1: $i ).
thf(p1_s3_subset_1_type,type,
p1_s3_subset_1: $i > $o ).
thf(v2_tex_4_type,type,
v2_tex_4: $i > $i > $o ).
thf(k4_enumset1_type,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_8_tex_4_type,type,
a_2_8_tex_4: $i > $i > $i ).
thf(a_2_0_tex_4_type,type,
a_2_0_tex_4: $i > $i > $i ).
thf(r4_connsp_1_type,type,
r4_connsp_1: $i > $i > $i > $o ).
thf(v2_connsp_2_type,type,
v2_connsp_2: $i > $i > $o ).
thf(m1_struct_0_type,type,
m1_struct_0: $i > $i > $i > $o ).
thf(k8_subset_1_type,type,
k8_subset_1: $i > $i ).
thf(r1_compts_1_type,type,
r1_compts_1: $i > $i > $i > $o ).
thf(a_2_6_tex_4_type,type,
a_2_6_tex_4: $i > $i > $i ).
thf(a_2_3_tex_4_type,type,
a_2_3_tex_4: $i > $i > $i ).
thf(k3_enumset1_type,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(v4_compts_1_type,type,
v4_compts_1: $i > $o ).
thf(f1_s1_subset_1_type,type,
f1_s1_subset_1: $i ).
thf(p1_s1_subset_1_type,type,
p1_s1_subset_1: $i > $o ).
thf(k5_enumset1_type,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_0_tex_2_type,type,
a_2_0_tex_2: $i > $i > $i ).
thf(f1_s2_subset_1_type,type,
f1_s2_subset_1: $i ).
thf(p1_s2_subset_1_type,type,
p1_s2_subset_1: $i > $o ).
thf(a_2_1_tex_4_type,type,
a_2_1_tex_4: $i > $i > $i ).
thf(f1_s4_subset_1_type,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_type,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_type,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_type,type,
f3_s4_subset_1: $i ).
thf(k6_enumset1_type,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_10_tex_4_type,type,
a_2_10_tex_4: $i > $i > $i ).
thf(k2_enumset1_type,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(1252,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(8536,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1646,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
thf(10647,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k9_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C ) @ ( k1_tarski @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_borsuk_1) ).
thf(4094,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k9_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C ) @ ( k1_tarski @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(581,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).
thf(4909,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r2_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) )
=> ( r2_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(621,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(5136,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(2075,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tops_1) ).
thf(12526,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075]) ).
thf(1618,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ~ ( ( v1_finset_1 @ C )
& ( r1_tarski @ C @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ~ ( ( r1_tarski @ E @ D )
& ( v1_finset_1 @ E )
& ( C
= ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_borsuk_1) ).
thf(10520,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ~ ( ( v1_finset_1 @ C )
& ( r1_tarski @ C @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ~ ( ( r1_tarski @ E @ D )
& ( v1_finset_1 @ E )
& ( C
= ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(668,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(5320,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( m1_subset_1 @ ( k7_eqrel_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_eqrel_1) ).
thf(2463,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( m1_subset_1 @ ( k7_eqrel_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_partfun1) ).
thf(2559,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(953,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_borsuk_1) ).
thf(6845,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(2124,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( B
= ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_t_0topsp) ).
thf(12738,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( B
= ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( B
= ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ C ) ) )
=> ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124]) ).
thf(1504,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m2_connsp_2 @ C @ A @ B )
<=> ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_connsp_2) ).
thf(9982,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m2_connsp_2 @ C @ A @ B )
=> ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) )
=> ( m2_connsp_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(1354,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v3_tex_3 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tex_3) ).
thf(9131,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v3_tex_3 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(6085,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1706,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(10917,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(1268,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tex_3) ).
thf(8618,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(1323,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ( v3_pre_topc @ ( k6_pre_topc @ A @ B ) @ A )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A )
& ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A )
& ( v3_tops_1 @ ( k6_pre_topc @ A @ B ) @ A )
& ( v1_tex_2 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_membered @ ( k6_pre_topc @ A @ B ) )
& ( v2_membered @ ( k6_pre_topc @ A @ B ) )
& ( v3_membered @ ( k6_pre_topc @ A @ B ) )
& ( v4_membered @ ( k6_pre_topc @ A @ B ) )
& ( v5_membered @ ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tex_4) ).
thf(8930,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ( v3_pre_topc @ ( k6_pre_topc @ A @ B ) @ A )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A )
& ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A )
& ( v3_tops_1 @ ( k6_pre_topc @ A @ B ) @ A )
& ( v1_tex_2 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_membered @ ( k6_pre_topc @ A @ B ) )
& ( v2_membered @ ( k6_pre_topc @ A @ B ) )
& ( v3_membered @ ( k6_pre_topc @ A @ B ) )
& ( v4_membered @ ( k6_pre_topc @ A @ B ) )
& ( v5_membered @ ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(508,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(4560,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1634,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tops_1) ).
thf(10609,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(1188,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B )
& ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc45_tex_2) ).
thf(8186,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B )
& ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(5116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1593,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ( v1_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_tops_3) ).
thf(10410,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ( v1_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(1956,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_tops_2) ).
thf(12055,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956]) ).
thf(608,axiom,
! [A: $i,B: $i] :
( ( ( v4_membered @ A )
& ( v4_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc25_membered) ).
thf(5088,plain,
! [A: $i,B: $i] :
( ( ( v4_membered @ A )
& ( v4_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1378,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ~ ( ~ ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ F @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tsep_1) ).
thf(9273,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ~ ( ~ ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ F @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(2084,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
<=> ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tex_2) ).
thf(12597,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_tex_2 @ B @ A )
=> ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) ) )
& ( ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) )
=> ( v4_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084]) ).
thf(919,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ( ( r4_tsep_1 @ A @ B @ D )
& ( r4_tsep_1 @ A @ C @ D ) )
=> ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D ) )
& ( ( ( r4_tsep_1 @ A @ D @ B )
& ( r4_tsep_1 @ A @ D @ C ) )
=> ( r4_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_tsep_1) ).
thf(6669,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ( ( r4_tsep_1 @ A @ B @ D )
& ( r4_tsep_1 @ A @ C @ D ) )
=> ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D ) )
& ( ( ( r4_tsep_1 @ A @ D @ B )
& ( r4_tsep_1 @ A @ D @ C ) )
=> ( r4_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(863,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( m1_borsuk_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ C @ E )
& ( r1_tarski @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ F @ B )
=> ( ( r1_xboole_0 @ F @ E )
| ( r1_tarski @ F @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_borsuk_1) ).
thf(6355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ C @ E )
& ( r1_tarski @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ F @ B )
=> ( ( r1_xboole_0 @ F @ E )
| ( r1_tarski @ F @ E ) ) ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ C @ E )
& ( r1_tarski @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ F @ B )
=> ( ( r1_xboole_0 @ F @ E )
| ( r1_tarski @ F @ E ) ) ) ) ) ) ) )
=> ( m1_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1957,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
& ( v1_tsp_1 @ C @ A ) )
=> ( ( ~ ( v4_pre_topc @ B @ A )
& ~ ( v4_pre_topc @ C @ A ) )
| ( v1_tsp_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tsp_1) ).
thf(12057,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
& ( v1_tsp_1 @ C @ A ) )
=> ( ( ~ ( v4_pre_topc @ B @ A )
& ~ ( v4_pre_topc @ C @ A ) )
| ( v1_tsp_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957]) ).
thf(2064,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(12490,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( ( v3_membered @ A )
& ( v3_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc24_membered) ).
thf(4450,plain,
! [A: $i,B: $i] :
( ( ( v3_membered @ A )
& ( v3_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1468,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc34_tex_2) ).
thf(9786,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(769,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_tex_2) ).
thf(5857,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_binop_1) ).
thf(2341,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r2_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) )
=> ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1805,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= ( k7_borsuk_1 @ A @ B @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_borsuk_1) ).
thf(11372,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= ( k7_borsuk_1 @ A @ B @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(407,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(4062,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(23,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(2263,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
& ( ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1970,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(12116,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970]) ).
thf(550,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(4729,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(397,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funcop_1) ).
thf(4022,plain,
! [A: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1992,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( v1_tops_2 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_borsuk_1) ).
thf(12189,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( v1_tops_2 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(1826,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
<=> ( v2_tops_2 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tops_2) ).
thf(11504,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tops_2 @ B @ A )
=> ( v2_tops_2 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v2_tops_2 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v1_tops_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(1659,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k1_setfam_1 @ ( a_2_0_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tex_4) ).
thf(10730,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k1_setfam_1 @ ( a_2_0_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(3477,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1844,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r1_connsp_2 @ A @ B )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
& ( r4_connsp_1 @ A @ C @ D )
& ( r2_hidden @ B @ D ) )
=> ( m1_connsp_2 @ D @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_connsp_2) ).
thf(11581,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_connsp_2 @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
& ( r4_connsp_1 @ A @ C @ D )
& ( r2_hidden @ B @ D ) )
=> ( m1_connsp_2 @ D @ A @ B ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
& ( r4_connsp_1 @ A @ C @ D )
& ( r2_hidden @ B @ D ) )
=> ( m1_connsp_2 @ D @ A @ B ) ) ) )
=> ( r1_connsp_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc29_membered) ).
thf(4852,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1662,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( v3_pre_topc @ B @ A ) )
=> ( r1_xboole_0 @ B @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tsep_1) ).
thf(10743,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( v3_pre_topc @ B @ A ) )
=> ( r1_xboole_0 @ B @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(6431,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(734,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(5676,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(856,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v1_tdlat_3 @ A ) )
=> ( v1_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tex_2) ).
thf(6317,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v1_tdlat_3 @ A ) )
=> ( v1_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_2) ).
thf(2427,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1711,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v2_t_0topsp @ A )
<=> ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tsp_1) ).
thf(10944,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ( v2_t_0topsp @ A )
=> ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) )
& ( ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) )
=> ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(2038,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v3_pre_topc @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( D = B )
=> ( v3_pre_topc @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_tops_2) ).
thf(12383,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v3_pre_topc @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( D = B )
=> ( v3_pre_topc @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ D )
=> ( ( r1_tarski @ E @ C )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
& ( E
= ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_borsuk_1) ).
thf(5778,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ D )
=> ( ( r1_tarski @ E @ C )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
& ( E
= ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(1573,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(10319,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(925,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(6690,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1231,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(8415,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1890,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k1_struct_0 @ A @ B ) )
=> ( v4_tex_4 @ ( k1_tex_2 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_tex_4) ).
thf(11763,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k1_struct_0 @ A @ B ) )
=> ( v4_tex_4 @ ( k1_tex_2 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).
thf(539,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relat_1) ).
thf(4682,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1239,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( v2_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) )
& ( l1_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_pcomps_1) ).
thf(8475,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( v2_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) )
& ( l1_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1315,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tex_2 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ? [D: $i] :
( ( v1_pre_topc @ D )
& ( v1_borsuk_1 @ D @ A )
& ( v3_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ( r3_tsep_2 @ A @ C @ D )
& ( m1_pre_topc @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tex_3) ).
thf(8887,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tex_2 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ? [D: $i] :
( ( v1_pre_topc @ D )
& ( v1_borsuk_1 @ D @ A )
& ( v3_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ( r3_tsep_2 @ A @ C @ D )
& ( m1_pre_topc @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(1810,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) )
& ( r2_hidden @ D @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_tsp_1) ).
thf(11394,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) )
& ( r2_hidden @ D @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) )
& ( r2_hidden @ D @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810]) ).
thf(1808,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) ) )
=> ~ ( ( v2_connsp_1 @ C @ ( k3_pre_topc @ A @ B ) )
& ( v3_pre_topc @ C @ ( k3_pre_topc @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v2_connsp_1 @ D @ A )
& ( C
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_connsp_2) ).
thf(11385,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) ) )
=> ~ ( ( v2_connsp_1 @ C @ ( k3_pre_topc @ A @ B ) )
& ( v3_pre_topc @ C @ ( k3_pre_topc @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v2_connsp_1 @ D @ A )
& ( C
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).
thf(1347,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B )
& ( v2_pre_topc @ B )
& ~ ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tex_4) ).
thf(9091,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B )
& ( v2_pre_topc @ B )
& ~ ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(1302,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(8828,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(1678,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
<=> ( ~ ( v3_struct_0 @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_pre_topc) ).
thf(10790,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
=> ( ~ ( v3_struct_0 @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) ) )
& ( ( ~ ( v3_struct_0 @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) )
=> ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(2108,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tex_3) ).
thf(12689,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108]) ).
thf(2082,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ( ( v2_t_0topsp @ B )
<=> ( ( v3_struct_0 @ B )
| ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_tsp_1) ).
thf(12549,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ( ( ( v2_t_0topsp @ B )
=> ( ( v3_struct_0 @ B )
| ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ) )
& ( ( ( v3_struct_0 @ B )
| ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) )
=> ( v2_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082]) ).
thf(1614,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tex_3) ).
thf(10507,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(3534,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1554,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v1_tops_1 @ D @ B )
<=> ( v1_tops_1 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tex_3) ).
thf(10234,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v1_tops_1 @ D @ B )
=> ( v1_tops_1 @ C @ A ) )
& ( ( v1_tops_1 @ C @ A )
=> ( v1_tops_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1985,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(12172,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
<=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_xboole_1) ).
thf(5297,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) )
& ( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( ( k12_mcart_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= C )
& ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_borsuk_1) ).
thf(6441,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( ( k12_mcart_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= C )
& ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(209,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(3108,plain,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(2837,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1462,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
<=> ( ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tex_3) ).
thf(9759,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) )
& ( ( ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(1115,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v2_tex_3 @ B @ A )
& ( v2_tex_3 @ C @ A ) )
=> ( ( v2_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tex_3) ).
thf(7813,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v2_tex_3 @ B @ A )
& ( v2_tex_3 @ C @ A ) )
=> ( ( v2_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1591,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v1_tex_3 @ B @ A )
<=> ( v1_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tex_3) ).
thf(10387,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v1_tex_3 @ B @ A )
=> ( v1_tops_1 @ C @ A ) )
& ( ( v1_tops_1 @ C @ A )
=> ( v1_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(1776,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tops_1) ).
thf(11224,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(780,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ C ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tex_2) ).
thf(5898,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ C ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(1789,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_connsp_2 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(11308,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_connsp_2 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(1124,axiom,
( ~ ( v3_struct_0 @ k22_borsuk_1 )
& ( v1_pre_topc @ k22_borsuk_1 )
& ( v2_pre_topc @ k22_borsuk_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_borsuk_1) ).
thf(7888,plain,
( ~ ( v3_struct_0 @ k22_borsuk_1 )
& ( v1_pre_topc @ k22_borsuk_1 )
& ( v2_pre_topc @ k22_borsuk_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v3_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_membered) ).
thf(4376,plain,
! [A: $i,B: $i] :
( ( v3_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v3_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(1798,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( k4_tsp_2 @ A @ B )
= ( k1_tsp_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_tsp_2) ).
thf(11350,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( k4_tsp_2 @ A @ B )
= ( k1_tsp_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(1441,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k2_pre_topc @ B ) )
= ( k2_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tops_2) ).
thf(9621,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k2_pre_topc @ B ) )
= ( k2_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(1235,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc27_membered) ).
thf(8450,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1176,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k1_pre_topc @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(8129,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k1_pre_topc @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(2940,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1134,axiom,
! [A: $i] :
( ( k2_pcomps_1 @ A )
= ( g1_pre_topc @ A @ ( k1_pcomps_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_pcomps_1) ).
thf(7935,plain,
! [A: $i] :
( ( k2_pcomps_1 @ A )
= ( g1_pre_topc @ A @ ( k1_pcomps_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(623,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
= ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funcop_1) ).
thf(5141,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
= ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1962,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ C )
& ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tops_3) ).
thf(12094,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ C )
& ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ C )
& ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(5225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1862,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_pre_topc @ ( k5_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_tex_4) ).
thf(11635,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_pre_topc @ ( k5_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862]) ).
thf(829,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
<=> ( ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_tex_3) ).
thf(6162,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) )
& ( ( ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1393,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(9351,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(7008,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ B @ C ) ) @ A )
= ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ C @ ( k10_funct_3 @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_borsuk_1) ).
thf(4311,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ B @ C ) ) @ A )
= ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ C @ ( k10_funct_3 @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(738,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tops_1) ).
thf(5696,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1489,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ D ) @ ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_borsuk_1) ).
thf(9924,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ D ) @ ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v2_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_binop_1) ).
thf(2644,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v2_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) )
=> ( v2_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(3230,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(5292,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( v3_struct_0 @ ( k2_tsep_1 @ A @ B @ C ) )
& ( v1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tsep_1) ).
thf(7958,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( v3_struct_0 @ ( k2_tsep_1 @ A @ B @ C ) )
& ( v1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
=> ( D
= ( k9_funct_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_2) ).
thf(9604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
=> ( D
= ( k9_funct_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(166,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( k5_pre_topc @ A @ B @ C @ D )
= ( k4_pre_topc @ B @ A @ ( k2_tops_2 @ A @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tops_2) ).
thf(2908,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( k5_pre_topc @ A @ B @ C @ D )
= ( k4_pre_topc @ B @ A @ ( k2_tops_2 @ A @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(767,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
<=> ( ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tex_3) ).
thf(5842,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) )
& ( ( ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1411,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(9456,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(907,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(6619,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1799,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m2_tsp_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_tsp_1) ).
thf(11353,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m2_tsp_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).
thf(1654,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_subset_1) ).
thf(10711,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(860,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tsp_1) ).
thf(6338,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( r1_subset_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r1_subset_1) ).
thf(6830,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( r1_subset_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(799,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(5982,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1342,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v1_borsuk_1 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc30_tex_2) ).
thf(9059,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v1_borsuk_1 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(1185,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_funct_1 @ ( k17_borsuk_1 @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_borsuk_1) ).
thf(8169,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_funct_1 @ ( k17_borsuk_1 @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_pre_topc @ ( k5_tex_4 @ A @ B ) )
& ( m1_pre_topc @ ( k5_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_tex_4) ).
thf(5669,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_pre_topc @ ( k5_tex_4 @ A @ B ) )
& ( m1_pre_topc @ ( k5_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(654,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( r1_tsep_1 @ A @ D @ C )
& ( r1_tsep_1 @ A @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_tsep_1) ).
thf(5265,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r3_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( r1_tsep_1 @ A @ D @ C )
& ( r1_tsep_1 @ A @ E @ B ) ) ) )
& ( ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( r1_tsep_1 @ A @ D @ C )
& ( r1_tsep_1 @ A @ E @ B ) ) )
=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(2138,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
| ( v2_tops_1 @ C @ A ) )
=> ( v2_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_tops_3) ).
thf(12789,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
| ( v2_tops_1 @ C @ A ) )
=> ( v2_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_zfmisc_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(7781,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_zfmisc_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(4614,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(2854,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1259,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_t_0topsp @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tsp_1) ).
thf(8563,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v2_t_0topsp @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) )
=> ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(1567,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_tops_1) ).
thf(10294,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(1530,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_borsuk_1) ).
thf(10125,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(1510,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_3) ).
thf(10039,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(1402,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( v2_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( v4_tdlat_3 @ A )
& ( v5_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tsp_1) ).
thf(9400,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( v2_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( v4_tdlat_3 @ A )
& ( v5_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(479,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(4408,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
<=> ( B
= ( k2_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(6602,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
=> ( B
= ( k2_subset_1 @ A ) ) )
& ( ( B
= ( k2_subset_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(5383,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(838,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(6214,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1333,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
<=> ~ ( ( r2_hidden @ A @ B )
<=> ( r2_hidden @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(9003,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
=> ~ ( ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ A @ C ) )
& ( ( r2_hidden @ A @ C )
=> ( r2_hidden @ A @ B ) ) ) )
& ( ~ ( ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ A @ C ) )
& ( ( r2_hidden @ A @ C )
=> ( r2_hidden @ A @ B ) ) )
=> ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(6194,plain,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1491,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(9933,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(5361,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( r2_hidden @ B @ A ) )
& ( ( r2_hidden @ B @ A )
=> ( m1_subset_1 @ B @ A ) ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( v1_xboole_0 @ B ) )
& ( ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(375,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
= ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funcop_1) ).
thf(3942,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
= ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1582,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tops_1) ).
thf(10346,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(1934,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tex_4) ).
thf(11962,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934]) ).
thf(2080,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(12545,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).
thf(1687,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( r1_connsp_1 @ A @ B @ C ) )
=> ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tsep_1) ).
thf(10827,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( r1_connsp_1 @ A @ B @ C ) )
=> ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(740,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
<=> ( r1_tarski @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ C ) ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tex_4) ).
thf(5708,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
=> ( r1_tarski @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ C ) ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) )
& ( ( r1_tarski @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ C ) ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1150,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(8012,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(362,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(3848,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(192,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_partfun1) ).
thf(3017,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_xboole_1) ).
thf(4543,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funcop_1) ).
thf(8101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(526,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(4633,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(287,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(3439,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1423,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( r1_tsep_1 @ A @ D @ C )
& ( r1_tsep_1 @ A @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_tsep_1) ).
thf(9526,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r3_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( r1_tsep_1 @ A @ D @ C )
& ( r1_tsep_1 @ A @ E @ B ) ) ) )
& ( ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( r1_tsep_1 @ A @ D @ C )
& ( r1_tsep_1 @ A @ E @ B ) ) )
=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(1412,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
<=> ( B
= ( k1_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(9460,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
=> ( B
= ( k1_subset_1 @ A ) ) )
& ( ( B
= ( k1_subset_1 @ A ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(1736,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tops_3) ).
thf(11072,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_partfun1) ).
thf(4418,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(4739,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1353,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(9127,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(6939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(2149,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_tex_3 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tex_3) ).
thf(12847,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_tex_3 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v2_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v1_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v2_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v4_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v5_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_realset2 @ ( k1_tex_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tex_2) ).
thf(5589,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v2_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v1_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v2_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v4_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v5_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_realset2 @ ( k1_tex_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).
thf(8150,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1094,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tex_3) ).
thf(7697,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1093,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(7695,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1525,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(10103,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1044,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ ( k17_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
& ( v5_pre_topc @ ( k17_borsuk_1 @ A @ B ) @ A @ ( k16_borsuk_1 @ A @ B ) )
& ( m2_relset_1 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_borsuk_1) ).
thf(7405,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ ( k17_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
& ( v5_pre_topc @ ( k17_borsuk_1 @ A @ B ) @ A @ ( k16_borsuk_1 @ A @ B ) )
& ( m2_relset_1 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(752,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( r4_tsep_1 @ A @ B @ C )
<=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ E @ ( k1_tsep_1 @ A @ B @ C ) ) @ C )
& ~ ( ~ ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_borsuk_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ F @ ( k1_tsep_1 @ A @ B @ C ) ) @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_tsep_1) ).
thf(5755,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( ( r4_tsep_1 @ A @ B @ C )
=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ E @ ( k1_tsep_1 @ A @ B @ C ) ) @ C )
& ~ ( ~ ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_borsuk_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ F @ ( k1_tsep_1 @ A @ B @ C ) ) @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) )
& ( ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ E @ ( k1_tsep_1 @ A @ B @ C ) ) @ C )
& ~ ( ~ ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_borsuk_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ F @ ( k1_tsep_1 @ A @ B @ C ) ) @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(325,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) )
=> ( ( r1_pcomps_1 @ A @ B )
=> ( ( k6_pcomps_1 @ A @ B )
= ( g1_metric_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pcomps_1) ).
thf(3648,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) )
=> ( ( r1_pcomps_1 @ A @ B )
=> ( ( k6_pcomps_1 @ A @ B )
= ( g1_metric_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1068,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_tex_2) ).
thf(7556,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ D ) ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(2918,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ B @ C @ D )
= ( k2_relat_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ B @ C @ D )
= ( k2_relat_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(499,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_relat_1) ).
thf(4528,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(222,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(3175,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1694,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
<=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r4_connsp_1 @ A @ B @ C ) )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_connsp_2) ).
thf(10864,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r4_connsp_1 @ A @ B @ C ) )
=> ( v3_pre_topc @ C @ A ) ) ) ) )
& ( ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r4_connsp_1 @ A @ B @ C ) )
=> ( v3_pre_topc @ C @ A ) ) ) )
=> ( v1_connsp_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(1428,axiom,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(9565,plain,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(2448,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(652,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v1_realset1 @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ( A
= ( k6_domain_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tex_2) ).
thf(5257,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( ( v1_realset1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ( A
= ( k6_domain_1 @ A @ B ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ( A
= ( k6_domain_1 @ A @ B ) ) )
=> ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(528,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(4638,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) )
& ( v2_tops_1 @ ( k3_tex_4 @ A @ B ) @ A )
& ( v1_tex_2 @ ( k3_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_membered @ ( k3_tex_4 @ A @ B ) )
& ( v2_membered @ ( k3_tex_4 @ A @ B ) )
& ( v3_membered @ ( k3_tex_4 @ A @ B ) )
& ( v4_membered @ ( k3_tex_4 @ A @ B ) )
& ( v5_membered @ ( k3_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_tex_4) ).
thf(3693,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) )
& ( v2_tops_1 @ ( k3_tex_4 @ A @ B ) @ A )
& ( v1_tex_2 @ ( k3_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_membered @ ( k3_tex_4 @ A @ B ) )
& ( v2_membered @ ( k3_tex_4 @ A @ B ) )
& ( v3_membered @ ( k3_tex_4 @ A @ B ) )
& ( v4_membered @ ( k3_tex_4 @ A @ B ) )
& ( v5_membered @ ( k3_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(811,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v4_tex_3 @ B @ A )
& ( v4_tex_3 @ C @ A ) )
=> ( v4_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tex_3) ).
thf(6078,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v4_tex_3 @ B @ A )
& ( v4_tex_3 @ C @ A ) )
=> ( v4_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k6_eqrel_1 @ A @ B @ C )
!= ( k6_eqrel_1 @ A @ B @ D ) )
& ~ ( r1_xboole_0 @ ( k6_eqrel_1 @ A @ B @ C ) @ ( k6_eqrel_1 @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_eqrel_1) ).
thf(4650,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k6_eqrel_1 @ A @ B @ C )
!= ( k6_eqrel_1 @ A @ B @ D ) )
& ~ ( r1_xboole_0 @ ( k6_eqrel_1 @ A @ B @ C ) @ ( k6_eqrel_1 @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r1_binop_1 @ A @ C @ B )
<=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_binop_1) ).
thf(2476,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
=> ( r2_binop_1 @ A @ C @ B ) )
& ( ( r2_binop_1 @ A @ C @ B )
=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1005,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v4_tex_3 @ B @ A )
<=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_tex_3) ).
thf(7147,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( v4_tex_3 @ B @ A )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ B @ C ) ) )
& ( ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ B @ C ) )
=> ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1781,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_xboole_0 @ ( k1_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tops_1) ).
thf(11239,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_xboole_0 @ ( k1_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(1395,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( r2_borsuk_1 @ A @ B )
<=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ C @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k23_borsuk_1 ) )
= D )
& ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k24_borsuk_1 ) ) @ ( u1_struct_0 @ B ) )
& ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ k22_borsuk_1 ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ E ) )
= D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_borsuk_1) ).
thf(9356,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( r2_borsuk_1 @ A @ B )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ C @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k23_borsuk_1 ) )
= D )
& ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k24_borsuk_1 ) ) @ ( u1_struct_0 @ B ) )
& ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ k22_borsuk_1 ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ E ) )
= D ) ) ) ) ) ) )
& ( ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ C @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k23_borsuk_1 ) )
= D )
& ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k24_borsuk_1 ) ) @ ( u1_struct_0 @ B ) )
& ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ k22_borsuk_1 ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ E ) )
= D ) ) ) ) ) )
=> ( r2_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1542,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tex_4) ).
thf(10170,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(755,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_metric_1) ).
thf(5782,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1371,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(9246,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(1142,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v1_tex_3 @ B @ A )
| ( v1_tex_3 @ C @ A ) )
=> ( ( v1_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_tex_3) ).
thf(7980,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v1_tex_3 @ B @ A )
| ( v1_tex_3 @ C @ A ) )
=> ( ( v1_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1887,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( k7_borsuk_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_borsuk_1) ).
thf(11756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( k7_borsuk_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887]) ).
thf(1580,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(10341,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(2143,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_tex_4) ).
thf(12816,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_1_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143]) ).
thf(1418,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( m1_borsuk_1 @ ( k19_borsuk_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_borsuk_1) ).
thf(9481,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( m1_borsuk_1 @ ( k19_borsuk_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(1464,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tex_2) ).
thf(9774,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(247,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_partfun1) ).
thf(3276,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(3370,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_relat_1) ).
thf(4679,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1397,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(9379,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(3281,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1449,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v2_tdlat_3 @ A ) )
=> ( v2_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tex_2) ).
thf(9657,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v2_tdlat_3 @ A ) )
=> ( v2_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(1075,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_tex_3) ).
thf(7592,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( v1_partfun1 @ E @ A @ B )
& ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_partfun1) ).
thf(5024,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( v1_partfun1 @ E @ A @ B )
& ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1761,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tex_4) ).
thf(11171,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(1651,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(10662,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(1579,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( v3_pre_topc @ D @ B )
& ( D
= ( k3_xboole_0 @ C @ ( u1_struct_0 @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tsp_1) ).
thf(10336,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( v3_pre_topc @ D @ B )
& ( D
= ( k3_xboole_0 @ C @ ( u1_struct_0 @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(1416,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ C @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_borsuk_1) ).
thf(9476,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ C @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(263,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
= ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funcop_1) ).
thf(3350,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
= ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(5740,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1708,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_tsp_1) ).
thf(10923,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(2107,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pcomps_1 @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k3_pcomps_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_pcomps_1) ).
thf(12686,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pcomps_1 @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k3_pcomps_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).
thf(345,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(3766,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( k6_eqrel_1 @ A @ B @ C )
= ( k10_relset_1 @ A @ A @ B @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_eqrel_1) ).
thf(2432,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( k6_eqrel_1 @ A @ B @ C )
= ( k10_relset_1 @ A @ A @ B @ ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1082,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( ( v4_tex_3 @ B @ A )
& ( v3_tex_3 @ C @ A ) )
| ( ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ C @ A ) ) )
=> ( v3_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tex_3) ).
thf(7637,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( ( v4_tex_3 @ B @ A )
& ( v3_tex_3 @ C @ A ) )
| ( ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ C @ A ) ) )
=> ( v3_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k9_relat_1 @ D @ A ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_partfun1) ).
thf(3915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k9_relat_1 @ D @ A ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(787,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc33_tex_2) ).
thf(5935,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1807,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k3_tex_4 @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tex_4) ).
thf(11382,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k3_tex_4 @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807]) ).
thf(1253,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(8539,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1929,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k1_tops_2 @ A @ B @ C ) @ ( k1_tops_2 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tops_2) ).
thf(11907,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k1_tops_2 @ A @ B @ C ) @ ( k1_tops_2 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).
thf(866,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_tsep_1 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tsep_1) ).
thf(6381,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_tsep_1 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1841,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ B )
=> ( v1_pcomps_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pcomps_1) ).
thf(11568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ B )
=> ( v1_pcomps_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).
thf(959,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_pcomps_1 @ A )
<=> ? [B: $i] :
( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( r1_pcomps_1 @ ( u1_struct_0 @ A ) @ B )
& ( ( k4_pcomps_1 @ ( k6_pcomps_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_pcomps_1) ).
thf(6872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v3_pcomps_1 @ A )
=> ? [B: $i] :
( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( r1_pcomps_1 @ ( u1_struct_0 @ A ) @ B )
& ( ( k4_pcomps_1 @ ( k6_pcomps_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( u1_pre_topc @ A ) ) ) )
& ( ? [B: $i] :
( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( r1_pcomps_1 @ ( u1_struct_0 @ A ) @ B )
& ( ( k4_pcomps_1 @ ( k6_pcomps_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( u1_pre_topc @ A ) ) )
=> ( v3_pcomps_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(4266,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1994,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( u1_struct_0 @ B ) )
& ( v2_tdlat_3 @ B ) )
=> ( v1_tex_4 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tex_4) ).
thf(12212,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( u1_struct_0 @ B ) )
& ( v2_tdlat_3 @ B ) )
=> ( v1_tex_4 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994]) ).
thf(1626,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( v2_tex_3 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tex_3) ).
thf(10545,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( v2_tex_3 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(1917,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v3_compts_1 @ A )
& ( v2_pcomps_1 @ A ) )
=> ( v5_compts_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_pcomps_1) ).
thf(11863,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v3_compts_1 @ A )
& ( v2_pcomps_1 @ A ) )
=> ( v5_compts_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( v2_tops_1 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) )
& ( v1_membered @ ( k1_tops_1 @ A @ B ) )
& ( v2_membered @ ( k1_tops_1 @ A @ B ) )
& ( v3_membered @ ( k1_tops_1 @ A @ B ) )
& ( v4_membered @ ( k1_tops_1 @ A @ B ) )
& ( v5_membered @ ( k1_tops_1 @ A @ B ) )
& ( v2_tops_1 @ ( k1_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_tops_1) ).
thf(2886,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( v2_tops_1 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) )
& ( v1_membered @ ( k1_tops_1 @ A @ B ) )
& ( v2_membered @ ( k1_tops_1 @ A @ B ) )
& ( v3_membered @ ( k1_tops_1 @ A @ B ) )
& ( v4_membered @ ( k1_tops_1 @ A @ B ) )
& ( v5_membered @ ( k1_tops_1 @ A @ B ) )
& ( v2_tops_1 @ ( k1_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(5903,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1173,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tex_2) ).
thf(8122,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(3809,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_subset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(2028,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v4_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pre_topc) ).
thf(12339,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v4_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028]) ).
thf(519,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funcop_1) ).
thf(4607,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1356,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k3_tarski @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_2_0_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_borsuk_1) ).
thf(9148,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k3_tarski @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_2_0_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(1629,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k3_pcomps_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( D
= ( k6_pre_topc @ A @ E ) )
& ( r2_hidden @ E @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pcomps_1) ).
thf(10559,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( C
= ( k3_pcomps_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( D
= ( k6_pre_topc @ A @ E ) )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( D
= ( k6_pre_topc @ A @ E ) )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( D
= ( k6_pre_topc @ A @ E ) )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( D
= ( k6_pre_topc @ A @ E ) )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k3_pcomps_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(85,axiom,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(2516,plain,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(2136,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_tsp_1) ).
thf(12785,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136]) ).
thf(904,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_tex_2) ).
thf(6608,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1334,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ( v1_pre_topc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pre_topc) ).
thf(9013,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ( v1_pre_topc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(850,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(6291,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(2098,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( a_2_8_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_8_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tex_4) ).
thf(12661,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( a_2_8_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_8_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3597,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1029,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ( m2_tsp_1 @ B @ C )
=> ( v2_t_0topsp @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tsp_1) ).
thf(7311,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ( m2_tsp_1 @ B @ C )
=> ( v2_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2869,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1558,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( v2_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_pre_topc) ).
thf(10248,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( v2_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(1535,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_pcomps_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r1_xboole_0 @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_pcomps_1) ).
thf(10142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_pcomps_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r1_xboole_0 @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r1_xboole_0 @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_0_pcomps_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( m1_subset_1 @ ( k14_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_borsuk_1) ).
thf(8214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( m1_subset_1 @ ( k14_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(2043,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v4_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tex_2) ).
thf(12417,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v4_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043]) ).
thf(1493,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(9938,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(2158,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tops_2) ).
thf(12869,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158]) ).
thf(355,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(3820,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(5553,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(789,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) @ ( k1_tops_2 @ A @ B @ C ) ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_2) ).
thf(5953,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) @ ( k1_tops_2 @ A @ B @ C ) ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1410,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_tex_3) ).
thf(9447,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(1341,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k20_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k20_borsuk_1) ).
thf(9056,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k20_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_subset_1) ).
thf(7241,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(3221,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_2) ).
thf(4546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ D )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1506,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(9989,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(108,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_tops_2 @ C @ A @ B )
<=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ D @ A )
<=> ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tops_2) ).
thf(2603,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_tops_2 @ C @ A @ B )
=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
=> ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B ) )
& ( ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B )
=> ( v4_pre_topc @ D @ A ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
=> ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B ) )
& ( ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B )
=> ( v4_pre_topc @ D @ A ) ) ) ) )
=> ( v3_tops_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_2) ).
thf(3195,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1359,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tsep_1) ).
thf(9172,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(1937,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
thf(11976,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).
thf(663,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(5306,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(571,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(4866,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(4563,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(2177,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) ) ) )
<=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_tex_4) ).
thf(12943,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ C ) ) ) ) )
& ( ( ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ C ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(6039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(1403,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(9410,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(1630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_9_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_9_tex_4) ).
thf(10587,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_9_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_9_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(1119,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( ( m1_pre_topc @ B @ C )
=> ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
& ( ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( m1_pre_topc @ B @ C ) )
& ( ( m1_pre_topc @ C @ B )
=> ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) )
& ( ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) )
=> ( m1_pre_topc @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tsep_1) ).
thf(7825,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( ( m1_pre_topc @ B @ C )
=> ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
& ( ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( m1_pre_topc @ B @ C ) )
& ( ( m1_pre_topc @ C @ B )
=> ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) )
& ( ( ( k2_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) )
=> ( m1_pre_topc @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1476,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) ) )
=> ( ( D
= ( k1_tops_2 @ A @ B @ C ) )
<=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ( ( r2_hidden @ E @ D )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ F @ C )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B )
= E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tops_2) ).
thf(9828,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) ) )
=> ( ( ( D
= ( k1_tops_2 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ F @ C )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B )
= E ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ F @ C )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B )
= E ) )
=> ( r2_hidden @ E @ D ) ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ F @ C )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B )
= E ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ F @ C )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B )
= E ) )
=> ( r2_hidden @ E @ D ) ) ) )
=> ( D
= ( k1_tops_2 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(1972,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
<=> ( v1_finset_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tops_2) ).
thf(12122,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_finset_1 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( v1_finset_1 @ B ) )
& ( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972]) ).
thf(1434,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ ( u1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pre_topc) ).
thf(9597,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ ( u1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(6538,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(213,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
=> ( C
= ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k6_domain_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_borsuk_1) ).
thf(3131,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
=> ( C
= ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k6_domain_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1769,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k6_pre_topc @ B @ D ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tops_3) ).
thf(11203,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k6_pre_topc @ B @ D ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(409,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(4070,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1043,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( k1_relat_1 @ ( k4_t_0topsp @ A ) )
= ( u1_struct_0 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k4_t_0topsp @ A ) ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_t_0topsp) ).
thf(7401,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( k1_relat_1 @ ( k4_t_0topsp @ A ) )
= ( u1_struct_0 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k4_t_0topsp @ A ) ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1715,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v5_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_tex_2 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_tex_2) ).
thf(10997,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v5_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_tex_2 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_tex_2 @ C @ A ) ) )
=> ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(1195,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k7_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) )
& ~ ( v2_tex_2 @ ( k7_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc21_tex_4) ).
thf(8225,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k7_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) )
& ~ ( v2_tex_2 @ ( k7_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ ( k6_eqrel_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_eqrel_1) ).
thf(2339,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ ( k6_eqrel_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1720,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ ( k3_tex_4 @ A @ B ) )
& ( r1_tarski @ B @ ( k3_tex_4 @ A @ C ) ) )
<=> ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tex_4) ).
thf(11025,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( r1_tarski @ C @ ( k3_tex_4 @ A @ B ) )
& ( r1_tarski @ B @ ( k3_tex_4 @ A @ C ) ) )
=> ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ C ) ) )
& ( ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ C ) )
=> ( ( r1_tarski @ C @ ( k3_tex_4 @ A @ B ) )
& ( r1_tarski @ B @ ( k3_tex_4 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(1427,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_4) ).
thf(9561,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(1904,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(11817,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(4415,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1118,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r3_tsep_2 @ A @ B @ C )
=> ( ( v2_tex_3 @ B @ A )
<=> ( v4_tex_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tex_3) ).
thf(7822,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r3_tsep_2 @ A @ B @ C )
=> ( ( ( v2_tex_3 @ B @ A )
=> ( v4_tex_3 @ C @ A ) )
& ( ( v4_tex_3 @ C @ A )
=> ( v2_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(6987,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(296,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(3495,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1559,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( v2_tops_1 @ C @ A ) )
=> ( v2_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_3) ).
thf(10251,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( v2_tops_1 @ C @ A ) )
=> ( v2_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(2116,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tops_3) ).
thf(12718,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2116]) ).
thf(1717,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tex_2) ).
thf(11010,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(875,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
& ( v1_tops_2 @ D @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( E
= ( k9_relat_1 @ ( k3_funct_3 @ C ) @ D ) )
=> ( v1_tops_2 @ E @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tops_2) ).
thf(6423,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
& ( v1_tops_2 @ D @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( E
= ( k9_relat_1 @ ( k3_funct_3 @ C ) @ D ) )
=> ( v1_tops_2 @ E @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1739,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tops_1) ).
thf(11087,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(1980,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tex_3 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tex_3) ).
thf(12154,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tops_1 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tops_1 @ C @ A ) ) )
=> ( v1_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v4_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_membered) ).
thf(4654,plain,
! [A: $i,B: $i] :
( ( v4_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v4_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(3617,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1550,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(10221,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(862,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(6350,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r1_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_binop_1) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r1_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) )
=> ( r1_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(3653,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1657,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(10719,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(1304,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( ( v5_tops_1 @ B @ A )
<=> ( v6_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_tops_1) ).
thf(8834,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( ( ( v5_tops_1 @ B @ A )
=> ( v6_tops_1 @ B @ A ) )
& ( ( v6_tops_1 @ B @ A )
=> ( v5_tops_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(26,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ ( k4_funcop_1 @ B @ A @ D ) ) )
=> ( ( k1_funct_1 @ ( k4_funcop_1 @ B @ A @ D ) @ C )
= ( k1_binop_1 @ B @ ( k1_funct_1 @ A @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funcop_1) ).
thf(2274,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ ( k4_funcop_1 @ B @ A @ D ) ) )
=> ( ( k1_funct_1 @ ( k4_funcop_1 @ B @ A @ D ) @ C )
= ( k1_binop_1 @ B @ ( k1_funct_1 @ A @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2041,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k4_tex_4 @ A @ C ) )
<=> ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_tarski @ ( k4_tex_4 @ A @ B ) @ D )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ C ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ B ) )
& ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tex_4) ).
thf(12394,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k4_tex_4 @ A @ C ) )
=> ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_tarski @ ( k4_tex_4 @ A @ B ) @ D )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ C ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ B ) )
& ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ D ) ) ) ) )
& ( ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_tarski @ ( k4_tex_4 @ A @ B ) @ D )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ C ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ B ) )
& ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ D ) ) ) )
=> ( r1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k4_tex_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).
thf(2167,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tops_3) ).
thf(12901,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167]) ).
thf(619,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_borsuk_1) ).
thf(5130,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(3410,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ~ ( r2_hidden @ D @ A )
<=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( A
= ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(7867,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ~ ( r2_hidden @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
& ( ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) )
=> ~ ( r2_hidden @ D @ A ) ) )
=> ( A
= ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k1_domain_1 @ A @ C @ E @ F ) )
= ( k1_domain_1 @ B @ C @ ( k8_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_borsuk_1) ).
thf(2185,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k1_domain_1 @ A @ C @ E @ F ) )
= ( k1_domain_1 @ B @ C @ ( k8_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(5160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1902,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
| ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tex_2) ).
thf(11812,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
| ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902]) ).
thf(1485,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_borsuk_1) ).
thf(9909,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(1192,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ~ ( r1_xboole_0 @ B @ C )
& ~ ( r1_tarski @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tex_4) ).
thf(8208,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ~ ( r1_xboole_0 @ B @ C )
& ~ ( r1_tarski @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ~ ( r1_xboole_0 @ B @ C )
& ~ ( r1_tarski @ B @ C ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(5182,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1179,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_borsuk_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D = E )
=> ( ( k5_pre_topc @ A @ B @ C @ D )
= ( k6_pre_topc @ A @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tex_2) ).
thf(8146,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_borsuk_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D = E )
=> ( ( k5_pre_topc @ A @ B @ C @ D )
= ( k6_pre_topc @ A @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(2085,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_10_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tex_4) ).
thf(12606,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_10_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085]) ).
thf(1452,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(9668,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(878,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( r1_borsuk_1 @ A @ B )
<=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_borsuk_1) ).
thf(6434,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( r1_borsuk_1 @ A @ B )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) )
& ( ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) )
=> ( r1_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(802,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(5989,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(891,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( D
= ( k1_tsep_1 @ A @ B @ C ) )
<=> ( ( u1_struct_0 @ D )
= ( k2_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tsep_1) ).
thf(6519,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ( D
= ( k1_tsep_1 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k2_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) )
& ( ( ( u1_struct_0 @ D )
= ( k2_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( D
= ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(983,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pcomps_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ C @ D )
& ( v3_pre_topc @ D @ A )
& ( v1_finset_1 @ ( a_3_0_pcomps_1 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pcomps_1) ).
thf(7000,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_pcomps_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ C @ D )
& ( v3_pre_topc @ D @ A )
& ( v1_finset_1 @ ( a_3_0_pcomps_1 @ A @ B @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ C @ D )
& ( v3_pre_topc @ D @ A )
& ( v1_finset_1 @ ( a_3_0_pcomps_1 @ A @ B @ D ) ) ) )
=> ( v1_pcomps_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( ( v1_membered @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc22_membered) ).
thf(4568,plain,
! [A: $i,B: $i] :
( ( ( v1_membered @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(3353,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(5836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(132,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
=> ( ( k1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) @ D )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funcop_1) ).
thf(2745,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
=> ( ( k1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) @ D )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(2114,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
=> ( ( k3_tarski @ ( a_2_0_tex_2 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tex_2) ).
thf(12713,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
=> ( ( k3_tarski @ ( a_2_0_tex_2 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( ( k8_eqrel_1 @ A @ B )
= ( k7_eqrel_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_eqrel_1) ).
thf(2571,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( ( k8_eqrel_1 @ A @ B )
= ( k7_eqrel_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1291,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r1_tsep_1 @ A @ B @ C )
<=> ( r1_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tsep_1) ).
thf(8753,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( r1_tsep_1 @ A @ B @ C )
=> ( r1_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
& ( ( r1_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( r1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(1290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(8748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(6130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1197,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v2_tex_3 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_tex_3) ).
thf(8235,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v2_tex_3 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(5746,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(4471,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(8252,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(1481,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v4_tex_3 @ B @ A )
<=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tex_3) ).
thf(9877,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( v4_tex_3 @ B @ A )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ B @ C ) ) )
& ( ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ B @ C ) )
=> ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(1318,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tops_1) ).
thf(8907,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) ) )
& ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_partfun1) ).
thf(2713,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(301,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ ( k6_domain_1 @ B @ D ) ) @ ( k3_funct_2 @ A @ C @ ( k7_funct_2 @ A @ B @ C @ E @ F ) @ ( k6_domain_1 @ C @ ( k8_funct_2 @ B @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_borsuk_1) ).
thf(3517,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ ( k6_domain_1 @ B @ D ) ) @ ( k3_funct_2 @ A @ C @ ( k7_funct_2 @ A @ B @ C @ E @ F ) @ ( k6_domain_1 @ C @ ( k8_funct_2 @ B @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funcop_1) ).
thf(3998,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
=> ( r1_tsep_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_tsep_1) ).
thf(3840,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
=> ( r1_tsep_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(5355,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(3463,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(2173,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v3_tex_2 @ C @ A )
<=> ( v1_tdlat_3 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tex_2) ).
thf(12920,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v3_tex_2 @ C @ A )
=> ( v1_tdlat_3 @ B ) )
& ( ( v1_tdlat_3 @ B )
=> ( v3_tex_2 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_1 @ A @ B @ C )
=> ( r4_tsep_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r4_tsep_1) ).
thf(5868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_1 @ A @ B @ C )
=> ( r4_tsep_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(3385,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(2147,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_2) ).
thf(12837,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tops_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v3_pre_topc @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v3_pre_topc @ C @ A ) ) )
=> ( v1_tops_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v3_membered @ B ) )
=> ( v3_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_membered) ).
thf(4353,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v3_membered @ B ) )
=> ( v3_membered @ ( k1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(773,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) @ ( k1_tops_2 @ A @ B @ C ) ) )
=> ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tops_2) ).
thf(5866,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) @ ( k1_tops_2 @ A @ B @ C ) ) )
=> ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(5214,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(718,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tex_2) ).
thf(5605,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1795,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k6_pre_topc @ A @ B )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_tex_4) ).
thf(11331,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k6_pre_topc @ A @ B )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k6_pre_topc @ A @ B )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(1317,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v5_pre_topc @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_pre_topc @ D @ B )
=> ( v3_pre_topc @ ( k5_pre_topc @ A @ B @ C @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_2) ).
thf(8902,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_pre_topc @ D @ B )
=> ( v3_pre_topc @ ( k5_pre_topc @ A @ B @ C @ D ) @ A ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_pre_topc @ D @ B )
=> ( v3_pre_topc @ ( k5_pre_topc @ A @ B @ C @ D ) @ A ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(2141,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( C = E ) )
=> ( ( ( v1_tops_1 @ D @ A )
& ( v1_tops_3 @ E @ B ) )
<=> ( v1_tops_3 @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tops_3) ).
thf(12804,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( C = E ) )
=> ( ( ( ( v1_tops_1 @ D @ A )
& ( v1_tops_3 @ E @ B ) )
=> ( v1_tops_3 @ C @ A ) )
& ( ( v1_tops_3 @ C @ A )
=> ( ( v1_tops_1 @ D @ A )
& ( v1_tops_3 @ E @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(4617,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(905,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ C )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B ) )
<=> ( r2_hidden @ ( k8_borsuk_1 @ A @ A @ C @ B ) @ ( k1_t_0topsp @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_t_0topsp) ).
thf(6611,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ C )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B ) )
=> ( r2_hidden @ ( k8_borsuk_1 @ A @ A @ C @ B ) @ ( k1_t_0topsp @ A ) ) )
& ( ( r2_hidden @ ( k8_borsuk_1 @ A @ A @ C @ B ) @ ( k1_t_0topsp @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ C )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(7124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(2023,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_3) ).
thf(12319,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023]) ).
thf(1528,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tsep_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tsep_1) ).
thf(10110,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v3_pre_topc @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v3_pre_topc @ C @ A ) ) )
=> ( v1_tsep_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(1839,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tops_3) ).
thf(11564,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839]) ).
thf(1494,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_tex_3) ).
thf(9941,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(6579,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1516,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
thf(10074,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(1784,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
| ( v3_pre_topc @ C @ A ) )
=> ( ( k3_tex_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tex_4) ).
thf(11247,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
| ( v3_pre_topc @ C @ A ) )
=> ( ( k3_tex_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(2093,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tops_1) ).
thf(12642,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093]) ).
thf(524,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(4622,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ B @ ( k2_funct_2 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) @ ( k2_funct_3 @ A @ B @ C ) @ D ) )
= ( k2_funct_2 @ A @ B @ C @ ( k5_setfam_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_borsuk_1) ).
thf(6272,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ B @ ( k2_funct_2 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) @ ( k2_funct_3 @ A @ B @ C ) @ D ) )
= ( k2_funct_2 @ A @ B @ C @ ( k5_setfam_1 @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(5397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(723,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tops_3) ).
thf(5622,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ C ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1899,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) )
& ( m1_pre_topc @ ( k7_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_tex_4) ).
thf(11802,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) )
& ( m1_pre_topc @ ( k7_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899]) ).
thf(1547,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tex_2) ).
thf(10206,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) )
=> ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(1999,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
& ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(12229,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
& ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999]) ).
thf(1746,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
=> ( v2_tops_2 @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_tops_2) ).
thf(11115,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
=> ( v2_tops_2 @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1849,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).
thf(11600,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m1_struct_0 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(2929,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(969,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_tex_2) ).
thf(6923,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
= ( k5_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).
thf(4551,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
= ( k5_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(2156,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_subset_1) ).
thf(12864,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2156]) ).
thf(763,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k1_tex_2 @ A @ C ) ) @ ( u1_pre_topc @ ( k1_tex_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tex_2) ).
thf(5829,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k1_tex_2 @ A @ C ) ) @ ( u1_pre_topc @ ( k1_tex_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_2) ).
thf(3014,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_2) ).
thf(2730,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1223,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
thf(8384,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1479,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_t_0topsp @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tsp_1) ).
thf(9869,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_t_0topsp @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ~ ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(7965,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ~ ( r2_hidden @ D @ C ) )
& ( ~ ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(6025,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1257,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ B @ C ) )
=> ( ( k5_borsuk_1 @ A @ B @ C @ D @ E )
= ( k10_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_borsuk_1) ).
thf(8558,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ B @ C ) )
=> ( ( k5_borsuk_1 @ A @ B @ C @ D @ E )
= ( k10_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
=> ( r3_tsep_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r3_tsep_1) ).
thf(5617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
=> ( r3_tsep_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1056,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tex_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tex_4) ).
thf(7509,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1028,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ D ) )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) @ ( k1_tops_2 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_tops_2) ).
thf(7309,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ D ) )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) @ ( k1_tops_2 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(3258,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(2135,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v4_tex_2 @ B @ A )
<=> ( v1_realset1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tex_2) ).
thf(12782,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v4_tex_2 @ B @ A )
=> ( v1_realset1 @ B ) )
& ( ( v1_realset1 @ B )
=> ( v4_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135]) ).
thf(1313,axiom,
? [A: $i] : ( l2_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(8870,plain,
? [A: $i] : ( l2_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1670,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
<=> ( v3_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tops_3) ).
thf(10764,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
=> ( v3_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v3_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v1_tops_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(1377,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r7_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_binop_1) ).
thf(9266,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r7_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) )
=> ( r7_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(1103,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( r2_hidden @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_pcomps_1) ).
thf(7733,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( r2_hidden @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(1882,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m1_struct_0 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_struct_0) ).
thf(11740,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m1_struct_0 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882]) ).
thf(1830,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( r1_tarski @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_tops_1) ).
thf(11533,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( r1_tarski @ B @ ( k2_tops_1 @ A @ B ) ) )
& ( ( r1_tarski @ B @ ( k2_tops_1 @ A @ B ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830]) ).
thf(1206,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ ( k3_tex_4 @ A @ B ) ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ ( k3_tex_4 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_tex_4) ).
thf(8293,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ ( k3_tex_4 @ A @ B ) ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ ( k3_tex_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1612,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B
!= ( k1_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_pre_topc) ).
thf(10497,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B
!= ( k1_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_binop_1) ).
thf(2829,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) )
=> ( v3_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_partfun1) ).
thf(4595,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1990,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tops_1) ).
thf(12185,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).
thf(1350,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_pre_topc) ).
thf(9103,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(1196,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) @ ( k13_borsuk_1 @ A @ B ) @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ~ ( ( r2_hidden @ E @ C )
& ( D
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) @ ( k10_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_borsuk_1) ).
thf(8229,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) @ ( k13_borsuk_1 @ A @ B ) @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ~ ( ( r2_hidden @ E @ C )
& ( D
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) @ ( k10_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(599,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( v4_tdlat_3 @ A )
& ( v5_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tsp_1) ).
thf(5013,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( v4_tdlat_3 @ A )
& ( v5_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(2083,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r2_tsep_1 @ A @ B @ C ) )
<=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tsep_1) ).
thf(12593,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( r1_xboole_0 @ B @ C )
& ( r2_tsep_1 @ A @ B @ C ) )
=> ( r1_connsp_1 @ A @ B @ C ) )
& ( ( r1_connsp_1 @ A @ B @ C )
=> ( ( r1_xboole_0 @ B @ C )
& ( r2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083]) ).
thf(832,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k2_tops_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D ) )
=> ( ~ ( r1_xboole_0 @ B @ D )
& ~ ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tops_1) ).
thf(6187,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_tops_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D ) )
=> ( ~ ( r1_xboole_0 @ B @ D )
& ~ ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D ) )
=> ( ~ ( r1_xboole_0 @ B @ D )
& ~ ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ D ) ) ) )
=> ( r2_hidden @ C @ ( k2_tops_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(2001,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(12237,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001]) ).
thf(1063,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc49_tex_2) ).
thf(7532,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1250,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) )
=> ( v1_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tex_2) ).
thf(8526,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) )
=> ( v1_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_2 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tsp_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_2 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(2178,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_2 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(5682,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(480,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(4411,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1513,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ D @ C )
<=> ( ( v3_pre_topc @ D @ A )
& ( v4_pre_topc @ D @ A )
& ( r2_hidden @ B @ D ) ) ) )
& ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_connsp_2) ).
thf(10046,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( ( v3_pre_topc @ D @ A )
& ( v4_pre_topc @ D @ A )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( v3_pre_topc @ D @ A )
& ( v4_pre_topc @ D @ A )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(1604,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tex_2) ).
thf(10454,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) )
= C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) )
= C ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
thf(4696,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(4205,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(5433,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) )
& ( ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) )
=> ( r1_tarski @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1383,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_tops_1 @ B @ A )
=> ( ( ( k2_tops_1 @ A @ B )
= ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
& ( ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_tops_1) ).
thf(9304,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_tops_1 @ B @ A )
=> ( ( ( k2_tops_1 @ A @ B )
= ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
& ( ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(1906,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( u1_struct_0 @ A ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ( v2_t_0topsp @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tsp_1) ).
thf(11821,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( u1_struct_0 @ A ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ( v2_t_0topsp @ A ) )
& ( ( v2_t_0topsp @ A )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906]) ).
thf(1792,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v2_tex_2 @ ( k1_tex_2 @ A @ B ) @ A )
& ( v3_realset2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tex_2) ).
thf(11314,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v2_tex_2 @ ( k1_tex_2 @ A @ B ) @ A )
& ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(1327,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r1_tsep_1 @ A @ B @ C ) )
=> ( ( r4_tsep_1 @ A @ B @ C )
<=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_tsep_1) ).
thf(8956,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r1_tsep_1 @ A @ B @ C ) )
=> ( ( ( r4_tsep_1 @ A @ B @ C )
=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) )
& ( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1433,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tex_2) ).
thf(9593,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(1053,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_t_0topsp @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ D @ A )
=> ( v3_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_t_0topsp) ).
thf(7492,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v1_t_0topsp @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ D @ A )
=> ( v3_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ D @ A )
=> ( v3_pre_topc @ ( k4_pre_topc @ A @ B @ C @ D ) @ B ) ) )
=> ( v1_t_0topsp @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1895,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
thf(11778,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
=> ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(4329,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
=> ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(2112,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ C @ A )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ C ) )
=> ( C
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tex_4) ).
thf(12706,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ C @ A )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ C ) )
=> ( C
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112]) ).
thf(1865,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k8_borsuk_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_borsuk_1) ).
thf(11656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k8_borsuk_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).
thf(229,axiom,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(3199,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(570,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(4857,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1638,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( ( r1_xboole_0 @ B @ C )
<=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tsep_1) ).
thf(10623,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
=> ( r1_connsp_1 @ A @ B @ C ) )
& ( ( r1_connsp_1 @ A @ B @ C )
=> ( r1_xboole_0 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v5_membered @ B ) )
=> ( v5_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_membered) ).
thf(2996,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v5_membered @ B ) )
=> ( v5_membered @ ( k1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1346,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
<=> ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tex_4) ).
thf(9088,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
=> ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) )
& ( ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(490,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_xboole_0 @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v1_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v2_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v3_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v4_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v5_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_tops_1) ).
thf(4454,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_xboole_0 @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v1_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v2_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v3_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v4_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) )
& ( v5_membered @ ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1825,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v1_tsp_1 @ C @ A ) )
=> ( v1_tsp_1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tsp_1) ).
thf(11500,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v1_tsp_1 @ C @ A ) )
=> ( v1_tsp_1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).
thf(1639,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m2_connsp_2 @ C @ A @ ( k1_struct_0 @ A @ B ) )
<=> ( m1_connsp_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_connsp_2) ).
thf(10626,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m2_connsp_2 @ C @ A @ ( k1_struct_0 @ A @ B ) )
=> ( m1_connsp_2 @ C @ A @ B ) )
& ( ( m1_connsp_2 @ C @ A @ B )
=> ( m2_connsp_2 @ C @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(917,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_t_0topsp @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ ( k3_t_0topsp @ A ) @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( u1_struct_0 @ B ) )
& ( C
= ( k4_borsuk_1 @ A @ ( k3_t_0topsp @ A ) @ B @ ( k4_t_0topsp @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_t_0topsp) ).
thf(6657,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_t_0topsp @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ ( k3_t_0topsp @ A ) @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( u1_struct_0 @ B ) )
& ( C
= ( k4_borsuk_1 @ A @ ( k3_t_0topsp @ A ) @ B @ ( k4_t_0topsp @ A ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_2) ).
thf(8158,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( v3_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v8_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v1_partfun1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A )
& ( m2_relset_1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_eqrel_1) ).
thf(4001,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( v3_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v8_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v1_partfun1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A )
& ( m2_relset_1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(3527,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1758,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( v4_pre_topc @ E @ B )
<=> ( v4_pre_topc @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tsep_1) ).
thf(11154,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( v4_pre_topc @ E @ B )
=> ( v4_pre_topc @ D @ A ) )
& ( ( v4_pre_topc @ D @ A )
=> ( v4_pre_topc @ E @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(3702,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
thf(3983,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(894,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ D )
=> ( ( r1_tarski @ E @ C )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( E
= ( k7_borsuk_1 @ A @ B @ F @ G ) ) ) ) ) )
=> ( r1_tarski @ ( k7_borsuk_1 @ A @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) @ ( k12_borsuk_1 @ A @ B ) @ D ) ) @ ( k6_setfam_1 @ ( u1_struct_0 @ B ) @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) @ ( k13_borsuk_1 @ A @ B ) @ D ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_borsuk_1) ).
thf(6534,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ D )
=> ( ( r1_tarski @ E @ C )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( E
= ( k7_borsuk_1 @ A @ B @ F @ G ) ) ) ) ) )
=> ( r1_tarski @ ( k7_borsuk_1 @ A @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) @ ( k12_borsuk_1 @ A @ B ) @ D ) ) @ ( k6_setfam_1 @ ( u1_struct_0 @ B ) @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) @ ( k13_borsuk_1 @ A @ B ) @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(7376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(2016,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_pre_topc @ ( k6_tex_4 @ A @ B ) @ ( k7_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_tex_4) ).
thf(12296,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_pre_topc @ ( k6_tex_4 @ A @ B ) @ ( k7_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).
thf(1965,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( ( v1_tsep_1 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tsep_1) ).
thf(12105,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( ( v1_tsep_1 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).
thf(1667,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
<=> ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tops_1) ).
thf(10757,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) )
& ( ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A )
=> ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(1518,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tops_2 @ B @ A )
& ( v1_tops_2 @ C @ A ) )
=> ( v1_tops_2 @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tops_2) ).
thf(10085,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tops_2 @ B @ A )
& ( v1_tops_2 @ C @ A ) )
=> ( v1_tops_2 @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(1676,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v1_tex_4 @ B @ A ) )
=> ( v1_tex_4 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tex_4) ).
thf(10786,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v1_tex_4 @ B @ A ) )
=> ( v1_tex_4 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(728,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tex_4) ).
thf(5650,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ D ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1153,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v1_tsep_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_tsep_1) ).
thf(8018,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v1_tsep_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(5311,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(800,axiom,
? [A: $i] : ( l1_metric_1 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_metric_1) ).
thf(5985,plain,
? [A: $i] : ( l1_metric_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(573,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(4871,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(561,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_tops_2 @ C @ A @ B )
=> ( v3_tops_2 @ ( k2_tops_2 @ A @ B @ C ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tops_2) ).
thf(4783,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_tops_2 @ C @ A @ B )
=> ( v3_tops_2 @ ( k2_tops_2 @ A @ B @ C ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1466,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tops_1) ).
thf(9781,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1387,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( r1_borsuk_1 @ A @ B )
=> ( r1_borsuk_1 @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) @ ( k21_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_borsuk_1) ).
thf(9319,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( r1_borsuk_1 @ A @ B )
=> ( r1_borsuk_1 @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) @ ( k21_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(2037,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_connsp_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_connsp_2) ).
thf(12379,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_connsp_2 @ A @ B ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_connsp_2 @ A @ B ) )
=> ( v1_connsp_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(6717,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(8196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(363,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(3851,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(2164,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
| ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_3) ).
thf(12888,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
| ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164]) ).
thf(1722,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k1_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tops_1) ).
thf(11036,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k1_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(1229,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tex_2) ).
thf(8411,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1384,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(9309,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(1861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(11632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861]) ).
thf(1760,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_connsp_2 @ B @ A )
<=> ( v1_connsp_2 @ ( k3_pre_topc @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_connsp_2) ).
thf(11168,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_connsp_2 @ B @ A )
=> ( v1_connsp_2 @ ( k3_pre_topc @ A @ B ) ) )
& ( ( v1_connsp_2 @ ( k3_pre_topc @ A @ B ) )
=> ( v2_connsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(1680,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(10799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(1490,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) )
=> ( v2_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tex_4) ).
thf(9928,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) )
=> ( v2_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(1301,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v5_pre_topc @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( v1_funct_1 @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( v5_pre_topc @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_borsuk_1) ).
thf(8823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v5_pre_topc @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( v1_funct_1 @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( v5_pre_topc @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k4_borsuk_1 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(1752,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tops_3) ).
thf(11136,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(1526,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k1_connsp_1 @ A @ B ) @ ( k1_connsp_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_connsp_2) ).
thf(10106,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k1_connsp_1 @ A @ B ) @ ( k1_connsp_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(134,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v1_relat_2 @ A )
& ( v1_relat_2 @ B ) )
=> ( ( v1_relat_2 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_2) ).
thf(2750,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v1_relat_2 @ A )
& ( v1_relat_2 @ B ) )
=> ( ( v1_relat_2 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ D )
& ( r1_partfun1 @ C @ D ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_2) ).
thf(3906,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ D )
& ( r1_partfun1 @ C @ D ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(3389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1961,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tops_3) ).
thf(12090,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961]) ).
thf(2027,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_tex_4) ).
thf(12330,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027]) ).
thf(2068,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v3_tops_1 @ D @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tops_3) ).
thf(12504,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v3_tops_1 @ D @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).
thf(786,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ( v2_t_0topsp @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_tsp_1) ).
thf(5929,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ( v2_t_0topsp @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(2104,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tops_1) ).
thf(12678,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).
thf(1791,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( v1_tops_1 @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(11312,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( v1_tops_1 @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(990,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B
!= ( k2_pre_topc @ A ) )
& ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
!= k1_xboole_0 )
& ( B
= ( k2_pre_topc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_pre_topc) ).
thf(7036,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B
!= ( k2_pre_topc @ A ) )
& ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
!= k1_xboole_0 )
& ( B
= ( k2_pre_topc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_relat_1) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ B @ C ) ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_1_borsuk_1 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k7_borsuk_1 @ B @ C @ E @ F ) )
& ( r1_tarski @ ( k7_borsuk_1 @ B @ C @ E @ F ) @ D )
& ( v3_pre_topc @ E @ B )
& ( v3_pre_topc @ F @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_borsuk_1) ).
thf(9897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ B @ C ) ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_borsuk_1 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k7_borsuk_1 @ B @ C @ E @ F ) )
& ( r1_tarski @ ( k7_borsuk_1 @ B @ C @ E @ F ) @ D )
& ( v3_pre_topc @ E @ B )
& ( v3_pre_topc @ F @ C ) ) )
& ( ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k7_borsuk_1 @ B @ C @ E @ F ) )
& ( r1_tarski @ ( k7_borsuk_1 @ B @ C @ E @ F ) @ D )
& ( v3_pre_topc @ E @ B )
& ( v3_pre_topc @ F @ C ) )
=> ( r2_hidden @ A @ ( a_3_1_borsuk_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(6648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1264,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(8595,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(8727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(5220,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(5210,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1500,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v4_pre_topc @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( D = B )
=> ( v4_pre_topc @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tops_2) ).
thf(9970,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v4_pre_topc @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( D = B )
=> ( v4_pre_topc @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(6755,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(2020,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v1_t_0topsp @ ( k4_t_0topsp @ A ) @ A @ ( k3_t_0topsp @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_t_0topsp) ).
thf(12311,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v1_t_0topsp @ ( k4_t_0topsp @ A ) @ A @ ( k3_t_0topsp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).
thf(943,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ D @ ( k18_borsuk_1 @ A @ B @ C ) )
& ~ ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_hidden @ E @ ( k2_pre_topc @ B ) )
& ( D
= ( k1_struct_0 @ A @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_borsuk_1) ).
thf(6777,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ D @ ( k18_borsuk_1 @ A @ B @ C ) )
& ~ ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_hidden @ E @ ( k2_pre_topc @ B ) )
& ( D
= ( k1_struct_0 @ A @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(610,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(5096,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1748,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_tops_3) ).
thf(11119,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(283,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(3421,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(677,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tex_2) ).
thf(5370,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1623,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k3_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tex_4) ).
thf(10538,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k3_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(2133,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v3_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_tops_3) ).
thf(12777,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v3_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133]) ).
thf(1814,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v1_tops_3 @ D @ B )
<=> ( v1_tops_3 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tex_3) ).
thf(11413,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v1_tops_3 @ D @ B )
=> ( v1_tops_3 @ C @ A ) )
& ( ( v1_tops_3 @ C @ A )
=> ( v1_tops_3 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814]) ).
thf(1946,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
| ( v1_tsp_1 @ C @ A ) )
=> ( v1_tsp_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tsp_1) ).
thf(12008,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
| ( v1_tsp_1 @ C @ A ) )
=> ( v1_tsp_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946]) ).
thf(1338,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(9035,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
& ! [F: $i,G: $i] :
( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_partfun1) ).
thf(5169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
& ! [F: $i,G: $i] :
( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(2067,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(12499,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067]) ).
thf(1584,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( m1_connsp_2 @ E @ A @ F )
& ( D = E )
& ( C = F ) )
=> ( m1_connsp_2 @ D @ ( k3_pre_topc @ A @ B ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_connsp_2) ).
thf(10350,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( m1_connsp_2 @ E @ A @ F )
& ( D = E )
& ( C = F ) )
=> ( m1_connsp_2 @ D @ ( k3_pre_topc @ A @ B ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(1389,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
=> ( r1_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tsep_1) ).
thf(9341,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
=> ( r1_tsep_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(1361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(9187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(1698,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( v1_tops_1 @ B @ A )
<=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tex_3) ).
thf(10895,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( ( v1_tops_1 @ B @ A )
=> ( v2_tops_1 @ C @ A ) )
& ( ( v2_tops_1 @ C @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_1) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(1812,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k2_tex_4 @ A @ C ) )
| ( ( k2_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_tex_4) ).
thf(11408,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k2_tex_4 @ A @ C ) )
| ( ( k2_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).
thf(544,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relat_1) ).
thf(4701,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(2154,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_tsp_1 @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_tsp_1) ).
thf(12860,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_tsp_1 @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154]) ).
thf(697,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tex_3) ).
thf(5489,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k4_pre_topc @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_pre_topc) ).
thf(6327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k4_pre_topc @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1847,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_pre_topc @ B )
=> ~ ( v2_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_tex_2) ).
thf(11596,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_pre_topc @ B )
=> ~ ( v2_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847]) ).
thf(1234,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(8443,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(1754,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tex_4) ).
thf(11143,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(6616,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(946,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( ~ ( ( v1_tex_3 @ B @ A )
& ( v1_tsep_1 @ B @ A ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( v4_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ~ ( ( r1_tsep_1 @ A @ C @ D )
& ( ( k1_tsep_1 @ A @ C @ D )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tex_3) ).
thf(6787,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( ~ ( ( v1_tex_3 @ B @ A )
& ( v1_tsep_1 @ B @ A ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( v4_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ~ ( ( r1_tsep_1 @ A @ C @ D )
& ( ( k1_tsep_1 @ A @ C @ D )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(4211,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1336,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tex_3) ).
thf(9024,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(1101,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_borsuk_1) ).
thf(7722,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_relat_1) ).
thf(3184,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1420,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(9501,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(183,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_tops_2 @ C @ A @ B )
<=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k6_pre_topc @ B @ D ) )
= ( k6_pre_topc @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tops_2) ).
thf(2982,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_tops_2 @ C @ A @ B )
=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k6_pre_topc @ B @ D ) )
= ( k6_pre_topc @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k6_pre_topc @ B @ D ) )
= ( k6_pre_topc @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) ) ) )
=> ( v3_tops_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1011,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
& ( v2_tops_2 @ D @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( E
= ( k9_relat_1 @ ( k3_funct_3 @ C ) @ D ) )
=> ( v2_tops_2 @ E @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_tops_2) ).
thf(7170,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
& ( v2_tops_2 @ D @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( E
= ( k9_relat_1 @ ( k3_funct_3 @ C ) @ D ) )
=> ( v2_tops_2 @ E @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(2129,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( v3_pre_topc @ B @ A )
| ( v4_pre_topc @ B @ A ) )
& ( v4_tex_2 @ B @ A )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tex_2) ).
thf(12762,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( v3_pre_topc @ B @ A )
| ( v4_pre_topc @ B @ A ) )
& ( v4_tex_2 @ B @ A )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129]) ).
thf(408,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(4065,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1321,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_tex_4 @ A @ B )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_tex_4) ).
thf(8924,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_tex_4 @ A @ B )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(272,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(3378,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1738,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_borsuk_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ C ) )
& ( A = D )
& ( r2_hidden @ ( k3_tarski @ D ) @ ( u1_pre_topc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_borsuk_1) ).
thf(11079,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_borsuk_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ C ) )
& ( A = D )
& ( r2_hidden @ ( k3_tarski @ D ) @ ( u1_pre_topc @ B ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ C ) )
& ( A = D )
& ( r2_hidden @ ( k3_tarski @ D ) @ ( u1_pre_topc @ B ) ) )
=> ( r2_hidden @ A @ ( a_2_2_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_binop_1) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(3995,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1549,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ( ( k6_pre_topc @ A @ B )
= ( k2_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tops_1) ).
thf(10216,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= ( k2_pre_topc @ A ) ) )
& ( ( ( k6_pre_topc @ A @ B )
= ( k2_pre_topc @ A ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(1249,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(8523,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(285,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_partfun1) ).
thf(3435,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1869,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( k6_pre_topc @ A @ D )
= ( k6_pre_topc @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tops_3) ).
thf(11677,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( k6_pre_topc @ A @ D )
= ( k6_pre_topc @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( ( v5_membered @ A )
& ( v5_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc26_membered) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( ( v5_membered @ A )
& ( v5_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1674,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tsp_1 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_tsp_1) ).
thf(10779,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tsp_1 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(1611,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k2_t_0topsp @ A )
= ( k8_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_t_0topsp) ).
thf(10494,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k2_t_0topsp @ A )
= ( k8_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(7657,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1487,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(9917,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(2922,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1426,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
<=> ( ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tops_3) ).
thf(9556,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= k1_xboole_0 ) )
& ( ( ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= k1_xboole_0 )
=> ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(5174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1246,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_borsuk_1) ).
thf(8508,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1556,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_4 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tex_4) ).
thf(10243,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_4 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(315,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tex_2) ).
thf(3582,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(190,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funcop_1) ).
thf(3011,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1913,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_tops_1) ).
thf(11852,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913]) ).
thf(2121,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tsep_1) ).
thf(12732,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(4604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(3857,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k6_eqrel_1 @ A @ ( k6_partfun1 @ A ) @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_eqrel_1) ).
thf(5157,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k6_eqrel_1 @ A @ ( k6_partfun1 @ A ) @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1836,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tex_2) ).
thf(11555,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).
thf(1572,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tsep_1) ).
thf(10313,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(6560,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(456,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tsep_1) ).
thf(4323,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_partfun1) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(593,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(4962,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1158,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc24_tex_2) ).
thf(8046,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(883,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tex_3) ).
thf(6482,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(2008,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tops_1) ).
thf(12275,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008]) ).
thf(1322,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_tops_1 @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tops_1) ).
thf(8927,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_tops_1 @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(1042,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tsp_1) ).
thf(7393,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(102,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(2574,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_xboole_1) ).
thf(5839,plain,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_relat_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k3_borsuk_1 @ A @ B @ C ) @ A @ B )
& ( v1_partfun1 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_borsuk_1) ).
thf(7745,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_relat_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k3_borsuk_1 @ A @ B @ C ) @ A @ B )
& ( v1_partfun1 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(341,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3720,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(2088,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v4_tex_2 @ C @ A ) )
=> ( v4_tex_2 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tex_2) ).
thf(12623,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v4_tex_2 @ C @ A ) )
=> ( v4_tex_2 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(4531,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(6139,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( m1_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(2052,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( r1_xboole_0 @ ( k2_tex_4 @ A @ C ) @ ( k3_tex_4 @ A @ B ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ C ) @ ( k3_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tex_4) ).
thf(12446,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( r1_xboole_0 @ ( k2_tex_4 @ A @ C ) @ ( k3_tex_4 @ A @ B ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ C ) @ ( k3_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052]) ).
thf(1721,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( m1_connsp_2 @ D @ ( k3_pre_topc @ A @ B ) @ C )
& ( D = E )
& ( C = F ) )
=> ( m1_connsp_2 @ E @ A @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_connsp_2) ).
thf(11032,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( m1_connsp_2 @ D @ ( k3_pre_topc @ A @ B ) @ C )
& ( D = E )
& ( C = F ) )
=> ( m1_connsp_2 @ E @ A @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(631,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(5167,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(2030,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r4_tsep_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( E
= ( u1_struct_0 @ C ) ) )
=> ( r2_tsep_1 @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_tsep_1) ).
thf(12350,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( r4_tsep_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( E
= ( u1_struct_0 @ C ) ) )
=> ( r2_tsep_1 @ A @ D @ E ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( E
= ( u1_struct_0 @ C ) ) )
=> ( r2_tsep_1 @ A @ D @ E ) ) ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030]) ).
thf(2174,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tsp_1) ).
thf(12927,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174]) ).
thf(794,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( ( v2_struct_0 @ A )
=> ( A
= ( g2_struct_0 @ ( u1_struct_0 @ A ) @ ( u2_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v2_struct_0) ).
thf(5968,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( ( v2_struct_0 @ A )
=> ( A
= ( g2_struct_0 @ ( u1_struct_0 @ A ) @ ( u2_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1123,axiom,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(7885,plain,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(1545,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ C )
=> ( v1_finset_1 @ ( k1_tops_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tops_2) ).
thf(10197,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ C )
=> ( v1_finset_1 @ ( k1_tops_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(507,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(4557,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r1_subset_1 @ A @ B )
=> ( r1_subset_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_subset_1) ).
thf(7518,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r1_subset_1 @ A @ B )
=> ( r1_subset_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( ( k9_borsuk_1 @ A @ B @ C @ D @ E @ F )
= ( k2_zfmisc_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_borsuk_1) ).
thf(10598,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( ( k9_borsuk_1 @ A @ B @ C @ D @ E @ F )
= ( k2_zfmisc_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(1045,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k1_t_0topsp @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ E @ A )
=> ( ( r2_hidden @ C @ E )
<=> ( r2_hidden @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_t_0topsp) ).
thf(7410,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k1_t_0topsp @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ E @ A )
=> ( ( ( r2_hidden @ C @ E )
=> ( r2_hidden @ D @ E ) )
& ( ( r2_hidden @ D @ E )
=> ( r2_hidden @ C @ E ) ) ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ E @ A )
=> ( ( ( r2_hidden @ C @ E )
=> ( r2_hidden @ D @ E ) )
& ( ( r2_hidden @ D @ E )
=> ( r2_hidden @ C @ E ) ) ) ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ E @ A )
=> ( ( ( r2_hidden @ C @ E )
=> ( r2_hidden @ D @ E ) )
& ( ( r2_hidden @ D @ E )
=> ( r2_hidden @ C @ E ) ) ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ E @ A )
=> ( ( ( r2_hidden @ C @ E )
=> ( r2_hidden @ D @ E ) )
& ( ( r2_hidden @ D @ E )
=> ( r2_hidden @ C @ E ) ) ) ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) )
=> ( B
= ( k1_t_0topsp @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1735,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( k12_borsuk_1 @ A @ B )
= ( k2_funct_3 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ A ) @ ( k9_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_borsuk_1) ).
thf(11069,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( k12_borsuk_1 @ A @ B )
= ( k2_funct_3 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ A ) @ ( k9_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(1562,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ D @ B )
=> ( ( k1_tops_1 @ B @ D )
= D ) )
& ( ( ( k1_tops_1 @ A @ C )
= C )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
thf(10258,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ D @ B )
=> ( ( k1_tops_1 @ B @ D )
= D ) )
& ( ( ( k1_tops_1 @ A @ C )
= C )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k10_relset_1 @ A @ B @ C @ A )
= ( k5_relset_1 @ A @ B @ C ) )
& ( ( k11_relset_1 @ A @ B @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_relset_1) ).
thf(4076,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k10_relset_1 @ A @ B @ C @ A )
= ( k5_relset_1 @ A @ B @ C ) )
& ( ( k11_relset_1 @ A @ B @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1540,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tex_2) ).
thf(10165,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(1959,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_compts_1 @ A )
=> ( v2_pcomps_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_pcomps_1) ).
thf(12068,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_compts_1 @ A )
=> ( v2_pcomps_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959]) ).
thf(771,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( r1_borsuk_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tex_2) ).
thf(5862,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( r1_borsuk_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(17,axiom,
! [A: $i] :
( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
=> ( ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
=> ( ( v1_funct_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
& ( v1_binop_1 @ A @ k1_xboole_0 )
& ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(2232,plain,
! [A: $i] :
( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
=> ( ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
=> ( ( v1_funct_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
& ( v1_binop_1 @ A @ k1_xboole_0 )
& ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1373,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_realset2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tex_2) ).
thf(9252,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(201,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_xboole_0 @ ( k1_pre_topc @ A ) )
& ( v3_pre_topc @ ( k1_pre_topc @ A ) @ A )
& ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A )
& ( v1_membered @ ( k1_pre_topc @ A ) )
& ( v2_membered @ ( k1_pre_topc @ A ) )
& ( v3_membered @ ( k1_pre_topc @ A ) )
& ( v4_membered @ ( k1_pre_topc @ A ) )
& ( v5_membered @ ( k1_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_tops_1) ).
thf(3054,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_xboole_0 @ ( k1_pre_topc @ A ) )
& ( v3_pre_topc @ ( k1_pre_topc @ A ) @ A )
& ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A )
& ( v1_membered @ ( k1_pre_topc @ A ) )
& ( v2_membered @ ( k1_pre_topc @ A ) )
& ( v3_membered @ ( k1_pre_topc @ A ) )
& ( v4_membered @ ( k1_pre_topc @ A ) )
& ( v5_membered @ ( k1_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1307,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(8842,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(701,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tsep_1) ).
thf(5519,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A ) ) )
=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1643,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) )
= ( k1_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tops_1) ).
thf(10639,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) )
= ( k1_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).
thf(7078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_binop_1) ).
thf(2621,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v1_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) )
=> ( v1_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_partfun1) ).
thf(2660,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(4059,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1608,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( v3_tex_4 @ B @ A ) )
=> ( B
= ( k2_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tex_4) ).
thf(10477,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( v3_tex_4 @ B @ A ) )
=> ( B
= ( k2_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_partfun1) ).
thf(2382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(3550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(2018,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k11_borsuk_1 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_borsuk_1) ).
thf(12300,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k11_borsuk_1 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018]) ).
thf(1360,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_tex_3) ).
thf(9175,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(282,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(3418,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(2102,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tops_1) ).
thf(12673,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(5122,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(2000,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(12232,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000]) ).
thf(1963,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( v5_pre_topc @ ( k3_borsuk_1 @ B @ A @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_borsuk_1) ).
thf(12100,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( v5_pre_topc @ ( k3_borsuk_1 @ B @ A @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(1872,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_tsep_1) ).
thf(11698,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).
thf(1104,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_tex_2) ).
thf(7735,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(335,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(3679,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1834,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v2_tex_3 @ B @ A )
<=> ( v1_tops_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tex_3) ).
thf(11545,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v2_tex_3 @ B @ A )
=> ( v1_tops_3 @ C @ A ) )
& ( ( v1_tops_3 @ C @ A )
=> ( v2_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834]) ).
thf(343,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3735,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1885,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_subset_1) ).
thf(11751,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).
thf(2003,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( m1_pre_topc @ B @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tsep_1) ).
thf(12260,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( m1_pre_topc @ B @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003]) ).
thf(949,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( l1_pre_topc @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ D @ A @ C )
& ( v5_pre_topc @ E @ C @ B ) )
=> ( v5_pre_topc @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tops_2) ).
thf(6820,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( l1_pre_topc @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ D @ A @ C )
& ( v5_pre_topc @ E @ C @ B ) )
=> ( v5_pre_topc @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(91,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v8_relat_2 @ A )
=> ( v8_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_relat_2) ).
thf(2541,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v8_relat_2 @ A )
=> ( v8_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1714,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v2_tops_1 @ C @ A )
<=> ( v2_tops_1 @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tops_3) ).
thf(10990,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v2_tops_1 @ C @ A )
=> ( v2_tops_1 @ D @ B ) )
& ( ( v2_tops_1 @ D @ B )
=> ( v2_tops_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(1017,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc21_tex_3) ).
thf(7229,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1337,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_funct_1 @ ( k13_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k13_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) )
& ( m2_relset_1 @ ( k13_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_borsuk_1) ).
thf(9031,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_funct_1 @ ( k13_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k13_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) )
& ( m2_relset_1 @ ( k13_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc32_membered) ).
thf(3610,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1319,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(8910,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k1_funct_2 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(4785,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k1_funct_2 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1772,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_3) ).
thf(11212,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(67,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( v5_membered @ B )
=> ( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_membered) ).
thf(2441,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( v5_membered @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(916,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k4_t_0topsp @ A ) )
& ( v1_funct_2 @ ( k4_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) )
& ( v5_pre_topc @ ( k4_t_0topsp @ A ) @ A @ ( k3_t_0topsp @ A ) )
& ( m2_relset_1 @ ( k4_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_t_0topsp) ).
thf(6652,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k4_t_0topsp @ A ) )
& ( v1_funct_2 @ ( k4_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) )
& ( v5_pre_topc @ ( k4_t_0topsp @ A ) @ A @ ( k3_t_0topsp @ A ) )
& ( m2_relset_1 @ ( k4_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1425,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc47_tex_2) ).
thf(9549,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
& ( r2_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_binop_1) ).
thf(2705,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
& ( r2_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( ( v2_membered @ A )
& ( v2_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc43_membered) ).
thf(4915,plain,
! [A: $i,B: $i] :
( ( ( v2_membered @ A )
& ( v2_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(2048,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(12437,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).
thf(57,axiom,
! [A: $i] :
( ( v5_membered @ A )
<=> ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v4_ordinal2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_membered) ).
thf(2409,plain,
! [A: $i] :
( ( ( v5_membered @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v4_ordinal2 @ B ) ) )
& ( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v4_ordinal2 @ B ) )
=> ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(492,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funcop_1) ).
thf(4466,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(2087,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
<=> ( v4_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tsep_1) ).
thf(12613,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( v4_pre_topc @ C @ A ) )
& ( ( v4_pre_topc @ C @ A )
=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(5734,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(2131,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ C @ B ) )
=> ( v3_tex_3 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tex_3) ).
thf(12773,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ C @ B ) )
=> ( v3_tex_3 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131]) ).
thf(991,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( v3_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_tex_3) ).
thf(7042,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( v3_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(724,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ~ ( v2_tdlat_3 @ A )
& ~ ( v3_tdlat_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_tsp_1) ).
thf(5630,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ~ ( v2_tdlat_3 @ A )
& ~ ( v3_tdlat_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).
thf(7989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
= ( k4_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).
thf(3972,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
= ( k4_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(3867,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_2) ).
thf(8329,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1891,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k5_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k5_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_tex_4) ).
thf(11766,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k5_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k5_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891]) ).
thf(475,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(4397,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(805,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v5_pre_topc @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) )
=> ? [F: $i] :
( ( m1_connsp_2 @ F @ A @ D )
& ( r1_tarski @ ( k4_pre_topc @ A @ B @ C @ F ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_borsuk_1) ).
thf(6032,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) )
=> ? [F: $i] :
( ( m1_connsp_2 @ F @ A @ D )
& ( r1_tarski @ ( k4_pre_topc @ A @ B @ C @ F ) @ E ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) )
=> ? [F: $i] :
( ( m1_connsp_2 @ F @ A @ D )
& ( r1_tarski @ ( k4_pre_topc @ A @ B @ C @ F ) @ E ) ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(7757,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_partfun1) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(6264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1292,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8756,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(1552,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tops_1) ).
thf(10229,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(2099,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) )
& ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ~ ( v1_tex_2 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_tex_4) ).
thf(12664,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) )
& ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ~ ( v1_tex_2 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(4252,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1918,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_tex_4) ).
thf(11865,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918]) ).
thf(761,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ~ ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc32_tex_2) ).
thf(5815,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ~ ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1120,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m2_relset_1 @ E @ A @ C ) )
=> ~ ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( k8_funct_2 @ A @ B @ D @ F )
= ( k8_funct_2 @ A @ B @ D @ G ) )
=> ( ( k8_funct_2 @ A @ C @ E @ F )
= ( k8_funct_2 @ A @ C @ E @ G ) ) ) ) )
& ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ F )
!= E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_borsuk_1) ).
thf(7834,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m2_relset_1 @ E @ A @ C ) )
=> ~ ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( k8_funct_2 @ A @ B @ D @ F )
= ( k8_funct_2 @ A @ B @ D @ G ) )
=> ( ( k8_funct_2 @ A @ C @ E @ F )
= ( k8_funct_2 @ A @ C @ E @ G ) ) ) ) )
& ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ F )
!= E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1440,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tops_1) ).
thf(9618,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(981,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tex_2) ).
thf(6990,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(743,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) @ ( k1_tops_2 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tops_2) ).
thf(5719,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) @ ( k1_tops_2 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(181,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_partfun1) ).
thf(2969,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(415,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( v2_funct_1 @ ( k2_tops_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tops_2) ).
thf(4091,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( v2_funct_1 @ ( k2_tops_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(2086,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) )
<=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ C ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tex_4) ).
thf(12608,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ C ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) ) ) )
& ( ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ C ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) ) )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(7640,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( r2_hidden @ ( k4_tarski @ D @ B ) @ C )
<=> ( ( k6_eqrel_1 @ A @ C @ D )
= ( k6_eqrel_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_eqrel_1) ).
thf(3134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( ( r2_hidden @ ( k4_tarski @ D @ B ) @ C )
=> ( ( k6_eqrel_1 @ A @ C @ D )
= ( k6_eqrel_1 @ A @ C @ B ) ) )
& ( ( ( k6_eqrel_1 @ A @ C @ D )
= ( k6_eqrel_1 @ A @ C @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(5085,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1092,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_2 @ A @ B @ C )
=> ( ( v4_tex_3 @ B @ A )
<=> ( v2_tex_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tex_3) ).
thf(7692,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_2 @ A @ B @ C )
=> ( ( ( v4_tex_3 @ B @ A )
=> ( v2_tex_3 @ C @ A ) )
& ( ( v2_tex_3 @ C @ A )
=> ( v4_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1592,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tops_1) ).
thf(10394,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(1627,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_connsp_1 @ A @ B )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_connsp_2) ).
thf(10548,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_connsp_1 @ A @ B )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(1316,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_1) ).
thf(8899,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(3814,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( ( k2_relat_1 @ D )
= B ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( v2_funct_1 @ D )
& ( v2_funct_1 @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_2) ).
thf(2528,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( ( k2_relat_1 @ D )
= B ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( v2_funct_1 @ D )
& ( v2_funct_1 @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1765,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F )
= ( k2_zfmisc_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_borsuk_1) ).
thf(11191,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F )
= ( k2_zfmisc_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(1020,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k1_struct_0 @ A @ B ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_tex_4) ).
thf(7244,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k1_struct_0 @ A @ B ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_relat_1) ).
thf(3514,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(336,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_partfun1) ).
thf(3682,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
thf(3286,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(900,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r3_tsep_2 @ A @ B @ C )
=> ( ( v1_tex_3 @ B @ A )
<=> ( v3_tex_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tex_3) ).
thf(6582,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r3_tsep_2 @ A @ B @ C )
=> ( ( ( v1_tex_3 @ B @ A )
=> ( v3_tex_3 @ C @ A ) )
& ( ( v3_tex_3 @ C @ A )
=> ( v1_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1289,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( r2_borsuk_1 @ A @ B )
=> ( r2_borsuk_1 @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) @ ( k21_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_borsuk_1) ).
thf(8746,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( r2_borsuk_1 @ A @ B )
=> ( r2_borsuk_1 @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) @ ( k21_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1613,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_pcomps_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pcomps_1) ).
thf(10502,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_pcomps_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(1072,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tops_1) ).
thf(7576,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(404,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tsep_1) ).
thf(4053,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(671,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v1_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tex_3) ).
thf(5341,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v1_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(33,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(2327,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(350,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_pre_topc @ A ) )
& ( v1_membered @ ( k1_pre_topc @ A ) )
& ( v2_membered @ ( k1_pre_topc @ A ) )
& ( v3_membered @ ( k1_pre_topc @ A ) )
& ( v4_membered @ ( k1_pre_topc @ A ) )
& ( v5_membered @ ( k1_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_pre_topc) ).
thf(3799,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_pre_topc @ A ) )
& ( v1_membered @ ( k1_pre_topc @ A ) )
& ( v2_membered @ ( k1_pre_topc @ A ) )
& ( v3_membered @ ( k1_pre_topc @ A ) )
& ( v4_membered @ ( k1_pre_topc @ A ) )
& ( v5_membered @ ( k1_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ D @ B @ A )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ A @ C )
=> ( m2_connsp_2 @ ( k5_pre_topc @ B @ A @ D @ E ) @ B @ ( k5_pre_topc @ B @ A @ D @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_borsuk_1) ).
thf(7097,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ D @ B @ A )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ A @ C )
=> ( m2_connsp_2 @ ( k5_pre_topc @ B @ A @ D @ E ) @ B @ ( k5_pre_topc @ B @ A @ D @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1279,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( k16_borsuk_1 @ A @ B ) )
<=> ( ( ( u1_struct_0 @ C )
= B )
& ( ( u1_pre_topc @ C )
= ( a_2_2_borsuk_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_borsuk_1) ).
thf(8683,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( C
= ( k16_borsuk_1 @ A @ B ) )
=> ( ( ( u1_struct_0 @ C )
= B )
& ( ( u1_pre_topc @ C )
= ( a_2_2_borsuk_1 @ A @ B ) ) ) )
& ( ( ( ( u1_struct_0 @ C )
= B )
& ( ( u1_pre_topc @ C )
= ( a_2_2_borsuk_1 @ A @ B ) ) )
=> ( C
= ( k16_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1658,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_8_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_8_tex_4) ).
thf(10721,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_8_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_8_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(6646,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(1563,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(10263,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(1352,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( v1_borsuk_1 @ D @ A )
& ( v3_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ( r4_tsep_2 @ A @ C @ D )
& ( m1_pre_topc @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tex_3) ).
thf(9113,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( v1_borsuk_1 @ D @ A )
& ( v3_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ( r4_tsep_2 @ A @ C @ D )
& ( m1_pre_topc @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(1297,axiom,
! [A: $i] :
( ( v1_pre_topc @ ( k2_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k2_pcomps_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_pcomps_1) ).
thf(8810,plain,
! [A: $i] :
( ( v1_pre_topc @ ( k2_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k2_pcomps_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(762,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_tex_2) ).
thf(5826,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_borsuk_1) ).
thf(4280,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(5391,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1202,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k5_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k5_tex_4 @ A @ B ) )
& ( v2_pre_topc @ ( k5_tex_4 @ A @ B ) )
& ( v2_tdlat_3 @ ( k5_tex_4 @ A @ B ) )
& ( v3_tdlat_3 @ ( k5_tex_4 @ A @ B ) )
& ( v4_tex_4 @ ( k5_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_tex_4) ).
thf(8255,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k5_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k5_tex_4 @ A @ B ) )
& ( v2_pre_topc @ ( k5_tex_4 @ A @ B ) )
& ( v2_tdlat_3 @ ( k5_tex_4 @ A @ B ) )
& ( v3_tdlat_3 @ ( k5_tex_4 @ A @ B ) )
& ( v4_tex_4 @ ( k5_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(739,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tex_3) ).
thf(5702,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k10_relat_1 @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_partfun1) ).
thf(3980,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k10_relat_1 @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(1578,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( ( k6_pre_topc @ A @ B )
!= k1_xboole_0 )
& ( B = k1_xboole_0 ) )
& ~ ( ( B != k1_xboole_0 )
& ( ( k6_pre_topc @ A @ B )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_pcomps_1) ).
thf(10330,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( ( k6_pre_topc @ A @ B )
!= k1_xboole_0 )
& ( B = k1_xboole_0 ) )
& ~ ( ( B != k1_xboole_0 )
& ( ( k6_pre_topc @ A @ B )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(1842,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_tex_4) ).
thf(11570,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_2_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(1303,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(8832,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(1295,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( m2_tsp_1 @ B @ A )
<=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_pre_topc @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tsp_1) ).
thf(8788,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( m2_tsp_1 @ B @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) )
=> ( v4_pre_topc @ C @ B ) ) ) ) ) )
& ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) )
=> ( v4_pre_topc @ C @ B ) ) ) ) )
=> ( m2_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(110,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( B
= ( k4_relat_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(2628,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( B
= ( k4_relat_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( B
= ( k4_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1324,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_4 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tex_4) ).
thf(8942,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_4 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(6427,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(149,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k4_funcop_1 @ B @ A @ C )
= ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funcop_1) ).
thf(2826,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k4_funcop_1 @ B @ A @ C )
= ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(6043,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_partfun1) ).
thf(3297,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r5_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_binop_1) ).
thf(3499,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r5_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(3065,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1432,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tex_4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tex_4) ).
thf(9586,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tex_4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
thf(5177,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(314,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3556,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( ( k4_relset_1 @ A @ B @ C )
= ( k4_relset_1 @ A @ B @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_partfun1) ).
thf(2872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( ( k4_relset_1 @ A @ B @ C )
= ( k4_relset_1 @ A @ B @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(5021,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(1939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(11980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939]) ).
thf(1154,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ~ ( v2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_tsp_1) ).
thf(8021,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ~ ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(2055,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m1_connsp_2 @ C @ A @ B )
<=> ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
thf(12461,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
=> ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) ) )
& ( ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) )
=> ( m1_connsp_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055]) ).
thf(1127,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
<=> ( m1_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_tsp_1) ).
thf(7902,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ( m2_tsp_1 @ B @ A )
=> ( m1_pre_topc @ B @ A ) )
& ( ( m1_pre_topc @ B @ A )
=> ( m2_tsp_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(2161,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
=> ( r2_tsep_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_tsep_1) ).
thf(12881,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
=> ( r2_tsep_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161]) ).
thf(1859,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tops_1) ).
thf(11629,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859]) ).
thf(1443,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tex_3) ).
thf(9626,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(458,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4327,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1399,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_borsuk_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( D = E )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k1_struct_0 @ B @ D ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tex_2) ).
thf(9391,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_borsuk_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( D = E )
=> ( ( k5_pre_topc @ A @ B @ C @ ( k1_struct_0 @ B @ D ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(1950,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k3_tarski @ ( a_2_0_tex_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tex_2) ).
thf(12025,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k3_tarski @ ( a_2_0_tex_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_partfun1) ).
thf(2200,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(5551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1822,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ ( k2_t_0topsp @ A ) )
=> ( ( r1_xboole_0 @ C @ B )
| ( r1_tarski @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_t_0topsp) ).
thf(11452,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ ( k2_t_0topsp @ A ) )
=> ( ( r1_xboole_0 @ C @ B )
| ( r1_tarski @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).
thf(952,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_tsep_1) ).
thf(6833,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r3_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) )
& ( ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) )
=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k4_relset_1 @ A @ B @ C )
= ( k1_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(4402,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k4_relset_1 @ A @ B @ C )
= ( k1_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1871,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v3_pre_topc @ C @ A )
<=> ( v3_pre_topc @ D @ B ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tops_3) ).
thf(11683,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v3_pre_topc @ C @ A )
=> ( v3_pre_topc @ D @ B ) )
& ( ( v3_pre_topc @ D @ B )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871]) ).
thf(614,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v2_membered @ B ) )
=> ( v2_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_membered) ).
thf(5113,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v2_membered @ B ) )
=> ( v2_membered @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(4942,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1508,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r1_connsp_2 @ A @ B )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r2_hidden @ B @ C ) )
=> ( r2_connsp_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_connsp_2) ).
thf(10035,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r1_connsp_2 @ A @ B )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r2_hidden @ B @ C ) )
=> ( r2_connsp_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(2168,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( v3_pre_topc @ D @ B )
& ( v4_tops_1 @ D @ B ) )
=> ( v6_tops_1 @ D @ B ) )
& ( ( v6_tops_1 @ C @ A )
=> ( ( v3_pre_topc @ C @ A )
& ( v4_tops_1 @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_tops_1) ).
thf(12905,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( v3_pre_topc @ D @ B )
& ( v4_tops_1 @ D @ B ) )
=> ( v6_tops_1 @ D @ B ) )
& ( ( v6_tops_1 @ C @ A )
=> ( ( v3_pre_topc @ C @ A )
& ( v4_tops_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(5658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(199,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( r1_tarski @ A @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_membered) ).
thf(3050,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( r1_tarski @ A @ k1_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(6267,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_binop_1) ).
thf(2492,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1703,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_pre_topc) ).
thf(10907,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(1857,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_xboole_0 @ B @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
=> ( ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tops_3) ).
thf(11624,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_xboole_0 @ B @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
=> ( ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857]) ).
thf(1482,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tex_3) ).
thf(9885,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1948,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v3_tex_2 @ B @ A ) )
=> ( v4_tex_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tex_2) ).
thf(12020,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v3_tex_2 @ B @ A ) )
=> ( v4_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948]) ).
thf(491,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(4461,plain,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(551,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_relat_1) ).
thf(4732,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1625,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
=> ( ( v3_pre_topc @ B @ A )
| ( v2_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tex_4) ).
thf(10543,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
=> ( ( v3_pre_topc @ B @ A )
| ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(2059,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v1_tops_1 @ C @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v1_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_tops_1) ).
thf(12478,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v1_tops_1 @ C @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v1_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059]) ).
thf(1607,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A )
& ~ ( v1_tex_2 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tex_4) ).
thf(10473,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A )
& ~ ( v1_tex_2 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(1743,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_5_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_5_tex_4) ).
thf(11101,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_5_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_5_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(2113,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(12709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2113]) ).
thf(1815,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) ) )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ B ) @ ( k7_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_tex_4) ).
thf(11420,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ C ) ) ) )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ B ) @ ( k7_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815]) ).
thf(1112,axiom,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).
thf(7767,plain,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1218,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_tex_2) ).
thf(8358,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(454,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(4316,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1751,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tops_1) ).
thf(11133,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(1730,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ~ ( v3_struct_0 @ ( k6_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_borsuk_1) ).
thf(11056,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ~ ( v3_struct_0 @ ( k6_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(1438,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tex_2) ).
thf(9608,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( v1_xboole_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(527,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(4636,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(1975,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_tops_3) ).
thf(12142,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).
thf(1740,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v3_tex_4 @ ( k2_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tex_4) ).
thf(11089,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v3_tex_4 @ ( k2_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(393,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v8_relat_2 @ A )
& ( v8_relat_2 @ B ) )
=> ( v8_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_relat_2) ).
thf(4012,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v8_relat_2 @ A )
& ( v8_relat_2 @ B ) )
=> ( v8_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(2034,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v3_tex_4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tex_4) ).
thf(12372,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v3_tex_4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034]) ).
thf(1533,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_t_0topsp @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tsp_1) ).
thf(10131,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v2_t_0topsp @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( r2_hidden @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) )
=> ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(810,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v3_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_tex_3) ).
thf(6075,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v3_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(2128,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( m1_pre_topc @ D @ A )
=> ! [E: $i] :
( ( m1_pre_topc @ E @ A )
=> ( ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( r3_tsep_1 @ A @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tsep_1) ).
thf(12760,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( m1_pre_topc @ D @ A )
=> ! [E: $i] :
( ( m1_pre_topc @ E @ A )
=> ( ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( r3_tsep_1 @ A @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128]) ).
thf(1217,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funcop_1) ).
thf(8354,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1237,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( C
= ( k2_borsuk_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_borsuk_1) ).
thf(8462,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( C
= ( k2_borsuk_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) )
=> ( C
= ( k2_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(1474,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A )
& ( v3_pre_topc @ D @ A )
& ( v1_tops_1 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) )
= B )
& ( r1_xboole_0 @ C @ D )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tops_3) ).
thf(9814,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A )
& ( v3_pre_topc @ D @ A )
& ( v1_tops_1 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) )
= B )
& ( r1_xboole_0 @ C @ D )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(2042,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ ( k2_tops_1 @ A @ B ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_tops_1) ).
thf(12414,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ ( k2_tops_1 @ A @ B ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042]) ).
thf(936,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc28_membered) ).
thf(6748,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(2073,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_tex_4 @ A @ B )
= ( a_2_3_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tex_4) ).
thf(12521,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_tex_4 @ A @ B )
= ( a_2_3_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073]) ).
thf(1692,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_borsuk_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_borsuk_1) ).
thf(10848,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_pre_topc @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v1_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(1880,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( B = k1_xboole_0 )
=> ( ( k3_pcomps_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pcomps_1) ).
thf(11734,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( B = k1_xboole_0 )
=> ( ( k3_pcomps_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).
thf(603,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(5053,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(3254,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1664,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( v2_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pre_topc) ).
thf(10748,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( v2_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(816,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tex_3) ).
thf(6101,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_partfun1) ).
thf(3413,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(2139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_10_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_10_tex_4) ).
thf(12792,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_10_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_10_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139]) ).
thf(144,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_partfun1) ).
thf(2801,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1139,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v1_tsep_1 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc29_tex_2) ).
thf(7962,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v1_tsep_1 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1335,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ~ ( v2_t_0topsp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tsp_1) ).
thf(9016,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ~ ( v2_t_0topsp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(4974,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(1712,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( v1_tops_3 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tops_3) ).
thf(10986,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( v1_tops_3 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(1149,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tops_1) ).
thf(8009,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(5615,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1924,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tex_4 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tsp_2) ).
thf(11884,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tex_4 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tex_4 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924]) ).
thf(974,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( C
= ( k5_tex_4 @ A @ B ) )
<=> ( ( u1_struct_0 @ C )
= ( k2_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_tex_4) ).
thf(6955,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( C
= ( k5_tex_4 @ A @ B ) )
=> ( ( u1_struct_0 @ C )
= ( k2_tex_4 @ A @ B ) ) )
& ( ( ( u1_struct_0 @ C )
= ( k2_tex_4 @ A @ B ) )
=> ( C
= ( k5_tex_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1495,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v5_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc23_tex_3) ).
thf(9945,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v5_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(44,axiom,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_relat_1) ).
thf(2359,plain,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(824,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tex_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tex_4) ).
thf(6133,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_pre_topc @ D )
& ( v2_pre_topc @ D )
& ( l1_pre_topc @ D ) )
=> ( ( r2_hidden @ A @ ( a_3_0_borsuk_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ D ) ) ) )
& ( A
= ( k5_setfam_1 @ ( u1_struct_0 @ D ) @ E ) )
& ( r1_tarski @ E @ ( a_2_1_borsuk_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_borsuk_1) ).
thf(8604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_pre_topc @ D )
& ( v2_pre_topc @ D )
& ( l1_pre_topc @ D ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_borsuk_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ D ) ) ) )
& ( A
= ( k5_setfam_1 @ ( u1_struct_0 @ D ) @ E ) )
& ( r1_tarski @ E @ ( a_2_1_borsuk_1 @ B @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ D ) ) ) )
& ( A
= ( k5_setfam_1 @ ( u1_struct_0 @ D ) @ E ) )
& ( r1_tarski @ E @ ( a_2_1_borsuk_1 @ B @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_0_borsuk_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(2069,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_compts_1 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ E @ C )
& ( r1_compts_1 @ A @ E @ D )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ E )
& ( r1_xboole_0 @ F @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_borsuk_1) ).
thf(12506,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_compts_1 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ E @ C )
& ( r1_compts_1 @ A @ E @ D )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ E )
& ( r1_xboole_0 @ F @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(7389,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(232,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(3218,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(402,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k5_funcop_1 @ B @ C @ A )
= ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funcop_1) ).
thf(4048,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k5_funcop_1 @ B @ C @ A )
= ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1212,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tex_2) ).
thf(8319,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(4525,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(542,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( v1_tsep_1 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_tsep_1) ).
thf(4693,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( v1_tsep_1 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
thf(4845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1152,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_struct_0 @ A @ D ) @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_borsuk_1) ).
thf(8016,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_struct_0 @ A @ D ) @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(688,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v1_borsuk_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tsep_1) ).
thf(5428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v1_borsuk_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1151,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_tops_1) ).
thf(8014,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1442,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(9624,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(1430,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_borsuk_1 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_borsuk_1) ).
thf(9576,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_borsuk_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= D ) ) )
=> ( v3_borsuk_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(382,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( v2_t_0topsp @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tsp_1) ).
thf(3963,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( v2_t_0topsp @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1601,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k3_tex_4 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tex_4) ).
thf(10445,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k3_tex_4 @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(797,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(5978,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1599,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_t_0topsp @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tsp_1) ).
thf(10434,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v2_t_0topsp @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(3119,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1912,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v3_tops_1 @ C @ A )
<=> ( v3_tops_1 @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tops_3) ).
thf(11845,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v3_tops_1 @ C @ A )
=> ( v3_tops_1 @ D @ B ) )
& ( ( v3_tops_1 @ D @ B )
=> ( v3_tops_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912]) ).
thf(678,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v3_realset2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_tex_2) ).
thf(5373,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v3_realset2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(239,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(3237,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1260,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(8572,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(2146,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
<=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
thf(12834,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146]) ).
thf(1668,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v2_tex_4 @ ( k1_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tex_4) ).
thf(10760,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v2_tex_4 @ ( k1_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(1298,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(8815,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(1788,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E )
& ( v3_tops_1 @ D @ A ) )
=> ( v3_tops_1 @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tops_3) ).
thf(11304,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E )
& ( v3_tops_1 @ D @ A ) )
=> ( v3_tops_1 @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ~ ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(5497,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ~ ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ~ ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1952,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m1_connsp_2 @ C @ A @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_connsp_2) ).
thf(12033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) )
=> ( m1_connsp_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(5475,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1463,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_tdlat_3 @ B )
=> ~ ( v2_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc23_tex_2) ).
thf(9772,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_tdlat_3 @ B )
=> ~ ( v2_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v5_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc36_membered) ).
thf(4898,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v5_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1831,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(11536,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).
thf(1987,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k1_struct_0 @ A @ B ) @ ( k2_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tex_4) ).
thf(12179,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k1_struct_0 @ A @ B ) @ ( k2_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987]) ).
thf(323,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(3622,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_borsuk_1) ).
thf(6720,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(6,axiom,
r1_tarski @ k5_numbers @ k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_numbers) ).
thf(2196,plain,
r1_tarski @ k5_numbers @ k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc31_membered) ).
thf(4513,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k3_subset_1 @ A @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
thf(6395,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k3_subset_1 @ A @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1898,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k2_tex_4 @ A @ B ) )
<=> ( ( k2_tex_4 @ A @ C )
= ( k2_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tex_4) ).
thf(11797,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_tex_4 @ A @ B ) )
=> ( ( k2_tex_4 @ A @ C )
= ( k2_tex_4 @ A @ B ) ) )
& ( ( ( k2_tex_4 @ A @ C )
= ( k2_tex_4 @ A @ B ) )
=> ( r2_hidden @ C @ ( k2_tex_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(4676,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(853,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tex_2) ).
thf(6299,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= C ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_2 @ D )
& ( v3_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ D @ C ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_eqrel_1) ).
thf(2460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_2 @ D )
& ( v3_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ D @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ D )
=> ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relset_1) ).
thf(2798,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1255,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k15_borsuk_1 @ A )
= ( k8_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_borsuk_1) ).
thf(8544,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k15_borsuk_1 @ A )
= ( k8_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3952,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(591,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r4_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_binop_1) ).
thf(4951,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r4_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1282,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
& ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
& ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funcop_1) ).
thf(8704,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
& ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
& ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc30_membered) ).
thf(4301,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(8631,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
& ! [G: $i,H: $i] :
( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(6175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
& ! [G: $i,H: $i] :
( ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ D )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ A ) ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1916,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k4_tex_4 @ A @ B ) )
& ( m1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tex_4) ).
thf(11860,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k4_tex_4 @ A @ B ) )
& ( m1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(5075,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(6967,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1688,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tops_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_3) ).
thf(10830,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tops_3 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v1_tops_3 @ C @ A ) ) )
=> ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(1080,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v1_tsep_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tsep_1) ).
thf(7631,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v1_tsep_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(783,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(5915,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1401,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(9397,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_partfun1) ).
thf(3407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(98,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_numbers) ).
thf(2561,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(2025,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_subset_1) ).
thf(12325,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025]) ).
thf(2109,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tops_1) ).
thf(12696,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) )
& ( ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109]) ).
thf(1920,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
<=> ( B
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tops_1) ).
thf(11869,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v5_tops_1 @ B @ A )
=> ( B
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) )
& ( ( B
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) )
=> ( v5_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920]) ).
thf(803,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( k6_pre_topc @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
<=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
thf(5992,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( k6_pre_topc @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1620,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(10528,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1589,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_tex_4) ).
thf(10381,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k7_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(1031,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tsep_1) ).
thf(7318,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(1288,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( k18_borsuk_1 @ A @ B @ C )
= ( k2_xboole_0 @ C @ ( a_2_3_borsuk_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_borsuk_1) ).
thf(8743,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( k18_borsuk_1 @ A @ B @ C )
= ( k2_xboole_0 @ C @ ( a_2_3_borsuk_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1147,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_tsp_1 @ B @ A )
<=> ( m1_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_tsp_1) ).
thf(7998,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( ( m1_tsp_1 @ B @ A )
=> ( m1_pre_topc @ B @ A ) )
& ( ( m1_pre_topc @ B @ A )
=> ( m1_tsp_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( r2_hidden @ C @ ( k6_eqrel_1 @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_eqrel_1) ).
thf(2419,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( r2_hidden @ C @ ( k6_eqrel_1 @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2092,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_tops_1) ).
thf(12639,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092]) ).
thf(2125,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v2_tops_2 @ C @ A ) )
=> ( v2_tops_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tops_2) ).
thf(12746,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v2_tops_2 @ C @ A ) )
=> ( v2_tops_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125]) ).
thf(1187,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc27_tex_3) ).
thf(8177,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(748,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_subset_1) ).
thf(5743,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( k2_relat_1 @ C )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_2) ).
thf(3441,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) ) )
& ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1673,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tops_1) ).
thf(10776,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(1637,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(10620,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(5263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1076,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ~ ( v3_tex_3 @ B @ A ) )
=> ( v1_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tex_3) ).
thf(7604,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ~ ( v3_tex_3 @ B @ A ) )
=> ( v1_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( C
= ( k7_eqrel_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ E @ A )
& ( D
= ( k6_eqrel_1 @ A @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_eqrel_1) ).
thf(4744,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( C
= ( k7_eqrel_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ A )
& ( D
= ( k6_eqrel_1 @ A @ B @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ A )
& ( D
= ( k6_eqrel_1 @ A @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ A )
& ( D
= ( k6_eqrel_1 @ A @ B @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ A )
& ( D
= ( k6_eqrel_1 @ A @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k7_eqrel_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1177,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ~ ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ A ) )
& ( v2_tex_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_tex_2) ).
thf(8132,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ~ ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ A ) )
& ( v2_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1725,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
=> ( v1_tops_2 @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tops_2) ).
thf(11046,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
=> ( v1_tops_2 @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(3032,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(910,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B )
& ( v2_pre_topc @ B )
& ~ ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tex_4) ).
thf(6630,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B )
& ( v2_pre_topc @ B )
& ~ ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1349,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(9100,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(1685,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_connsp_2 @ B @ A @ C )
=> ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_connsp_2) ).
thf(10823,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_connsp_2 @ B @ A @ C )
=> ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(1544,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tex_4) ).
thf(10195,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(1328,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(8968,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(1379,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pre_topc) ).
thf(9288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(2151,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k3_pre_topc @ A @ B ) )
& ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pre_topc) ).
thf(12853,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k3_pre_topc @ A @ B ) )
& ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
thf(2349,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1050,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(7480,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ~ ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_2) ).
thf(3723,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ~ ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1539,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
=> ( r1_connsp_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tsep_1) ).
thf(10163,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
=> ( r1_connsp_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(896,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tex_3) ).
thf(6541,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1070,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tdlat_3 @ B )
=> ~ ( v4_tex_4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tex_4) ).
thf(7572,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tdlat_3 @ B )
=> ~ ( v4_tex_4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(7976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(2118,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( v4_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v4_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_tops_1) ).
thf(12724,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( v4_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v4_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118]) ).
thf(1030,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_pre_topc @ A @ B )
<=> ( ( k2_pre_topc @ A )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
thf(7313,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_pre_topc @ A @ B )
=> ( ( k2_pre_topc @ A )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) ) )
& ( ( ( k2_pre_topc @ A )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( r1_pre_topc @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(847,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc31_tex_3) ).
thf(6275,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(7523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(1522,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( m1_pre_topc @ ( k1_tex_2 @ A @ B ) @ ( k5_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tex_4) ).
thf(10094,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( m1_pre_topc @ ( k1_tex_2 @ A @ B ) @ ( k5_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_tex_2 @ B @ A )
<=> ( B
!= ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
thf(6724,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( ( v1_tex_2 @ B @ A )
=> ( B
!= ( k3_tarski @ A ) ) )
& ( ( B
!= ( k3_tarski @ A ) )
=> ( v1_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1375,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tex_2) ).
thf(9260,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(70,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
<=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(2450,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
=> ( v2_funct_1 @ A ) )
& ( ( v2_funct_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(3541,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1728,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tops_3) ).
thf(11052,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(1569,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tex_4) ).
thf(10306,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(7913,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(241,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_tops_2 @ C @ A @ B )
<=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_pre_topc @ A @ B @ C @ ( k6_pre_topc @ A @ D ) )
= ( k6_pre_topc @ B @ ( k4_pre_topc @ A @ B @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tops_2) ).
thf(3242,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_tops_2 @ C @ A @ B )
=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_pre_topc @ A @ B @ C @ ( k6_pre_topc @ A @ D ) )
= ( k6_pre_topc @ B @ ( k4_pre_topc @ A @ B @ C @ D ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_pre_topc @ A @ B @ C @ ( k6_pre_topc @ A @ D ) )
= ( k6_pre_topc @ B @ ( k4_pre_topc @ A @ B @ C @ D ) ) ) ) )
=> ( v3_tops_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(1707,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_pre_topc @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pcomps_1) ).
thf(10919,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_pre_topc @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1364,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tex_2) ).
thf(9200,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(1883,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tex_4 @ B @ A )
& ~ ( v1_realset1 @ B )
& ( v1_tsp_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tsp_1) ).
thf(11742,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tex_4 @ B @ A )
& ~ ( v1_realset1 @ B )
& ( v1_tsp_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v2_funct_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_2) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v2_funct_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(667,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tex_2) ).
thf(5317,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1851,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_tex_4) ).
thf(11608,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851]) ).
thf(1277,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).
thf(8673,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(328,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
=> ( ( v1_membered @ A )
& ( v2_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_membered) ).
thf(3656,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
=> ( ( v1_membered @ A )
& ( v2_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1907,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v6_compts_1 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_borsuk_1) ).
thf(11828,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v6_compts_1 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907]) ).
thf(1392,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(9348,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(2091,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tsp_1) ).
thf(12632,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091]) ).
thf(1595,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tex_4) ).
thf(10423,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k7_eqrel_1 @ A @ B ) )
& ( v1_setfam_1 @ ( k7_eqrel_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_eqrel_1) ).
thf(2519,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k7_eqrel_1 @ A @ B ) )
& ( v1_setfam_1 @ ( k7_eqrel_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(4384,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(5149,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1214,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tex_3) ).
thf(8326,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(2045,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( v4_pre_topc @ C @ A )
& ( r2_hidden @ B @ C )
& ( r1_tarski @ C @ ( k1_connsp_2 @ A @ B ) ) )
=> ( C
= ( k1_connsp_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_connsp_2) ).
thf(12429,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( v4_pre_topc @ C @ A )
& ( r2_hidden @ B @ C )
& ( r1_tarski @ C @ ( k1_connsp_2 @ A @ B ) ) )
=> ( C
= ( k1_connsp_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).
thf(1386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(9316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(1982,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ D )
& ( r1_connsp_1 @ A @ C @ D ) )
<=> ( r1_connsp_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tsep_1) ).
thf(12164,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( r1_connsp_1 @ A @ B @ D )
& ( r1_connsp_1 @ A @ C @ D ) )
=> ( r1_connsp_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) )
& ( ( r1_connsp_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D )
=> ( ( r1_connsp_1 @ A @ B @ D )
& ( r1_connsp_1 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_2 @ E )
& ( v3_relat_2 @ E )
& ( v8_relat_2 @ E )
& ( v1_partfun1 @ E @ A @ A )
& ( m2_relset_1 @ E @ A @ A ) )
=> ( ( ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ E @ C ) )
& ( r2_hidden @ D @ ( k6_eqrel_1 @ A @ E @ C ) ) )
=> ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_eqrel_1) ).
thf(5134,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_2 @ E )
& ( v3_relat_2 @ E )
& ( v8_relat_2 @ E )
& ( v1_partfun1 @ E @ A @ A )
& ( m2_relset_1 @ E @ A @ A ) )
=> ( ( ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ E @ C ) )
& ( r2_hidden @ D @ ( k6_eqrel_1 @ A @ E @ C ) ) )
=> ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(2077,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
thf(12532,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077]) ).
thf(1802,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tops_1) ).
thf(11360,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) )
=> ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(1483,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( ( k3_subset_1 @ A @ D )
= ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_borsuk_1) ).
thf(9893,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( ( k3_subset_1 @ A @ D )
= ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( A = k1_xboole_0 )
=> ( ( k7_eqrel_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_eqrel_1) ).
thf(2355,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( A = k1_xboole_0 )
=> ( ( k7_eqrel_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1105,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= C )
=> ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_pre_topc) ).
thf(7738,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= C )
=> ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_partfun1) ).
thf(2465,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1537,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_tops_1 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_tops_1) ).
thf(10158,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_tops_1 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(1993,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( r2_hidden @ C @ A )
<=> ( p1_s2_subset_1 @ C ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( r2_hidden @ C @ B )
<=> ( p1_s2_subset_1 @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_subset_1) ).
thf(12191,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( ( r2_hidden @ C @ A )
=> ( p1_s2_subset_1 @ C ) )
& ( ( p1_s2_subset_1 @ C )
=> ( r2_hidden @ C @ A ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( ( r2_hidden @ C @ B )
=> ( p1_s2_subset_1 @ C ) )
& ( ( p1_s2_subset_1 @ C )
=> ( r2_hidden @ C @ B ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).
thf(1565,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ( v3_pcomps_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_pcomps_1) ).
thf(10285,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ( v3_pcomps_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(4829,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A )
=> ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(584,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(4934,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_funct_1) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(100,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v1_relat_2 @ A )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_2) ).
thf(2566,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v1_relat_2 @ A )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(4717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(967,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r1_tsep_1 @ A @ B @ C ) )
=> ( ( r4_tsep_1 @ A @ B @ C )
<=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_tsep_1) ).
thf(6908,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r1_tsep_1 @ A @ B @ C ) )
=> ( ( ( r4_tsep_1 @ A @ B @ C )
=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) )
& ( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(5217,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(138,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( v5_membered @ B )
=> ( ( A = B )
<=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_membered) ).
thf(2766,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( v5_membered @ B )
=> ( ( ( A = B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) ) ) )
& ( ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(2482,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1640,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_borsuk_1) ).
thf(10629,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(873,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(6418,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1163,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(8090,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1437,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(9607,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(259,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(3333,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1628,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r1_connsp_2 @ A @ B )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ C @ A @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ B )
& ( v2_connsp_1 @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_connsp_2) ).
thf(10550,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_connsp_2 @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ C @ A @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ B )
& ( v2_connsp_1 @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ C @ A @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ B )
& ( v2_connsp_1 @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ) )
=> ( r1_connsp_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(1210,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( C
= ( k1_tex_2 @ A @ B ) )
<=> ( ( u1_struct_0 @ C )
= ( k1_struct_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tex_2) ).
thf(8307,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( C
= ( k1_tex_2 @ A @ B ) )
=> ( ( u1_struct_0 @ C )
= ( k1_struct_0 @ A @ B ) ) )
& ( ( ( u1_struct_0 @ C )
= ( k1_struct_0 @ A @ B ) )
=> ( C
= ( k1_tex_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1852,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( m1_subset_1 @ ( k4_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_pcomps_1) ).
thf(11610,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( m1_subset_1 @ ( k4_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(5603,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(2101,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_tops_3) ).
thf(12671,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101]) ).
thf(1742,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_4 @ B @ A )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B )
& ( B
= ( k2_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_tex_4) ).
thf(11093,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_4 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B )
& ( B
= ( k2_tex_4 @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B )
& ( B
= ( k2_tex_4 @ A @ C ) ) )
=> ( v3_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(2006,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k1_struct_0 @ A @ B ) )
=> ( v3_tex_4 @ ( k1_struct_0 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tex_4) ).
thf(12270,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k1_struct_0 @ A @ B ) )
=> ( v3_tex_4 @ ( k1_struct_0 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006]) ).
thf(374,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(3920,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( m1_eqrel_1 @ ( k7_eqrel_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_eqrel_1) ).
thf(2272,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( m1_eqrel_1 @ ( k7_eqrel_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_2) ).
thf(7333,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(136,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(2756,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(3162,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1012,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_eqrel_1 @ ( k15_borsuk_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_borsuk_1) ).
thf(7174,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_eqrel_1 @ ( k15_borsuk_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(4223,plain,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t183_relat_1) ).
thf(2370,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(231,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(3215,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(8127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1648,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tex_4 @ B @ A )
=> ( v1_tex_4 @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tex_4) ).
thf(10651,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tex_4 @ B @ A )
=> ( v1_tex_4 @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2926,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1453,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( ~ ( ( v3_tex_3 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( v1_borsuk_1 @ D @ A )
& ( v3_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ~ ( ( ( k2_tsep_1 @ A @ C @ D )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( ( k1_tsep_1 @ A @ C @ D )
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tex_3) ).
thf(9684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( ~ ( ( v3_tex_3 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( v1_borsuk_1 @ D @ A )
& ( v3_tex_3 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ~ ( ( ( k2_tsep_1 @ A @ C @ D )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( ( k1_tsep_1 @ A @ C @ D )
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4081,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1091,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v2_tex_3 @ B @ A )
| ( v2_tex_3 @ C @ A ) )
=> ( ( v2_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tex_3) ).
thf(7687,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( v2_tex_3 @ B @ A )
| ( v2_tex_3 @ C @ A ) )
=> ( ( v2_tex_3 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(764,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tex_2) ).
thf(5833,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1159,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) )
& ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ( v4_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ( v2_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v1_tex_2 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_membered @ ( k1_tops_1 @ A @ B ) )
& ( v2_membered @ ( k1_tops_1 @ A @ B ) )
& ( v3_membered @ ( k1_tops_1 @ A @ B ) )
& ( v4_membered @ ( k1_tops_1 @ A @ B ) )
& ( v5_membered @ ( k1_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_tex_4) ).
thf(8049,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) )
& ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ( v4_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ( v2_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v1_tex_2 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_membered @ ( k1_tops_1 @ A @ B ) )
& ( v2_membered @ ( k1_tops_1 @ A @ B ) )
& ( v3_membered @ ( k1_tops_1 @ A @ B ) )
& ( v4_membered @ ( k1_tops_1 @ A @ B ) )
& ( v5_membered @ ( k1_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r2_hidden @ B @ A )
=> ( r2_hidden @ ( k4_tarski @ B @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_eqrel_1) ).
thf(2748,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r2_hidden @ B @ A )
=> ( r2_hidden @ ( k4_tarski @ B @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(2050,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( v3_pre_topc @ B @ A ) )
=> ( v3_tex_4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tex_4) ).
thf(12442,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( v3_pre_topc @ B @ A ) )
=> ( v3_tex_4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).
thf(1733,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tops_3) ).
thf(11065,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(1892,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) )
=> ( ( v3_pre_topc @ B @ ( k3_t_0topsp @ A ) )
<=> ( r2_hidden @ ( k3_tarski @ B ) @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_t_0topsp) ).
thf(11769,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) ) )
=> ( ( ( v3_pre_topc @ B @ ( k3_t_0topsp @ A ) )
=> ( r2_hidden @ ( k3_tarski @ B ) @ ( u1_pre_topc @ A ) ) )
& ( ( r2_hidden @ ( k3_tarski @ B ) @ ( u1_pre_topc @ A ) )
=> ( v3_pre_topc @ B @ ( k3_t_0topsp @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc33_membered) ).
thf(5198,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(958,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v1_borsuk_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_tsep_1) ).
thf(6869,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v1_borsuk_1 @ ( k1_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(886,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k2_t_0topsp @ A ) )
& ( m1_eqrel_1 @ ( k2_t_0topsp @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_t_0topsp) ).
thf(6497,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k2_t_0topsp @ A ) )
& ( m1_eqrel_1 @ ( k2_t_0topsp @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(6409,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(5557,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(422,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(4184,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1989,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_borsuk_1 @ ( k15_borsuk_1 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_borsuk_1) ).
thf(12183,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_borsuk_1 @ ( k15_borsuk_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989]) ).
thf(986,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tsep_1) ).
thf(7020,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(2788,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(3834,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1681,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v1_tops_1 @ B @ A ) )
=> ( v1_tops_3 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tops_3) ).
thf(10802,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v1_tops_1 @ B @ A ) )
=> ( v1_tops_3 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(1774,axiom,
! [A: $i] :
( ( u1_struct_0 @ ( k2_pcomps_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_pcomps_1) ).
thf(11216,plain,
! [A: $i] :
( ( u1_struct_0 @ ( k2_pcomps_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(1767,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k1_tops_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tops_2) ).
thf(11197,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k1_tops_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(235,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ( v2_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).
thf(3225,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ( v2_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( ( k12_mcart_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ A @ ( k9_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= C )
& ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ B @ ( k10_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_borsuk_1) ).
thf(5711,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( ( k12_mcart_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ A @ ( k9_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= C )
& ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ B @ ( k10_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_2) ).
thf(2546,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_partfun1) ).
thf(2761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(2011,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_borsuk_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_borsuk_1) ).
thf(12282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_borsuk_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).
thf(1191,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( r1_xboole_0 @ B @ C ) )
=> ( C
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_pre_topc) ).
thf(8205,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( r1_xboole_0 @ B @ C ) )
=> ( C
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_tarski @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(5402,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(7052,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) )
& ( ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) )
=> ( m1_eqrel_1 @ B @ A ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( m1_eqrel_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(2123,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( a_3_1_pcomps_1 @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_pcomps_1) ).
thf(12736,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( a_3_1_pcomps_1 @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123]) ).
thf(1219,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ A ) )
<=> ( r2_hidden @ C @ ( u1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_borsuk_1) ).
thf(8361,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( ( ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ C @ ( u1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) )
& ( ( r2_hidden @ C @ ( u1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) )
=> ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(2165,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_tops_3) ).
thf(12891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165]) ).
thf(1455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_borsuk_1 @ A @ B @ C )
= ( k2_funcop_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_borsuk_1) ).
thf(9716,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_borsuk_1 @ A @ B @ C )
= ( k2_funcop_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(1897,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( v1_tops_1 @ C @ A )
& ( v1_tops_3 @ E @ B ) )
<=> ( v1_tops_3 @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tops_3) ).
thf(11787,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( ( v1_tops_1 @ C @ A )
& ( v1_tops_3 @ E @ B ) )
=> ( v1_tops_3 @ D @ A ) )
& ( ( v1_tops_3 @ D @ A )
=> ( ( v1_tops_1 @ C @ A )
& ( v1_tops_3 @ E @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).
thf(1587,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tops_1) ).
thf(10377,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(2963,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(2062,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_tex_2 @ B @ A ) )
=> ( v3_tex_2 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_tex_2) ).
thf(12486,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_tex_2 @ B @ A ) )
=> ( v3_tex_2 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).
thf(1642,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_subset_1 )
=> ( ( r2_hidden @ B @ A )
<=> ( p1_s3_subset_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1) ).
thf(10635,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_subset_1 )
=> ( ( ( r2_hidden @ B @ A )
=> ( p1_s3_subset_1 @ B ) )
& ( ( p1_s3_subset_1 @ B )
=> ( r2_hidden @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(865,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(6378,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_partfun1) ).
thf(2402,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1927,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tops_3) ).
thf(11901,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(4448,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(6688,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1203,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tsep_1) ).
thf(8262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(2031,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ B )
=> ( ( k6_pre_topc @ A @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k3_pcomps_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_pcomps_1) ).
thf(12361,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_finset_1 @ B )
=> ( ( k6_pre_topc @ A @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k3_pcomps_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031]) ).
thf(1520,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
=> ( v4_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_2) ).
thf(10090,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
=> ( v4_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(778,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(5887,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(1832,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] : ( m1_borsuk_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_borsuk_1) ).
thf(11539,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] : ( m1_borsuk_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(6311,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(1355,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc18_tex_2) ).
thf(9139,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(776,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tex_4) ).
thf(5872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1270,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(8626,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(1505,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( k1_tops_1 @ A @ D )
= ( k1_tops_1 @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tops_3) ).
thf(9985,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( k1_tops_1 @ A @ D )
= ( k1_tops_1 @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(1283,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v2_pcomps_1 @ A )
& ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A )
& ( r1_tarski @ B @ E )
& ( r2_hidden @ D @ F )
& ( r1_xboole_0 @ E @ F ) ) ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_pcomps_1) ).
thf(8708,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v2_pcomps_1 @ A )
& ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A )
& ( r1_tarski @ B @ E )
& ( r2_hidden @ D @ F )
& ( r1_xboole_0 @ E @ F ) ) ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(1143,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7985,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(5679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1690,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_pre_topc) ).
thf(10840,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(744,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tex_4) ).
thf(5722,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_partfun1) ).
thf(2556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(104,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(2585,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1170,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v4_tex_3 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tex_3) ).
thf(8110,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v4_tex_3 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1756,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tex_4) ).
thf(11148,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(1009,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(7165,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1340,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( D
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ A ) @ ( k9_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ C ) )
=> ( v3_pre_topc @ D @ A ) )
& ( ( E
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) @ ( k10_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ C ) )
=> ( v3_pre_topc @ E @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_borsuk_1) ).
thf(9049,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( D
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ A ) @ ( k9_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ C ) )
=> ( v3_pre_topc @ D @ A ) )
& ( ( E
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) @ ( k10_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ C ) )
=> ( v3_pre_topc @ E @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(1695,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v4_tex_2 @ B @ A ) )
=> ( v1_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tex_2) ).
thf(10872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v4_tex_2 @ B @ A ) )
=> ( v1_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(1184,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
<=> ( ( k1_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tsep_1) ).
thf(8164,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( m1_pre_topc @ B @ C )
=> ( ( k1_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) )
& ( ( ( k1_tsep_1 @ A @ B @ C )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) )
=> ( m1_pre_topc @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(5327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(1744,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ( v1_realset1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tex_2) ).
thf(11110,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ( v1_realset1 @ B ) )
& ( ( v1_realset1 @ B )
=> ( v3_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(1405,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(9416,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(1983,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
=> ( v3_pre_topc @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tops_2) ).
thf(12168,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
=> ( v3_pre_topc @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983]) ).
thf(1274,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(8641,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(540,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(4685,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1876,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ C )
& ( r1_tarski @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_connsp_2) ).
thf(11710,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ C )
& ( r1_tarski @ D @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ C )
& ( r1_tarski @ D @ B ) ) ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v2_tsp_1 @ B @ A )
<=> ( v2_t_0topsp @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_v2_tsp_1) ).
thf(6203,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( v2_tsp_1 @ B @ A )
=> ( v2_t_0topsp @ B ) )
& ( ( v2_t_0topsp @ B )
=> ( v2_tsp_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1365,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_tex_2) ).
thf(9203,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(4874,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(699,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tex_3) ).
thf(5508,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1106,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r1_subset_1 @ A @ B )
<=> ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_subset_1) ).
thf(7742,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( ( r1_subset_1 @ A @ B )
=> ( r1_xboole_0 @ A @ B ) )
& ( ( r1_xboole_0 @ A @ B )
=> ( r1_subset_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(8040,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1006,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_tsep_1) ).
thf(7155,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(1571,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tops_1) ).
thf(10310,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(5855,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(649,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_tops_1) ).
thf(5230,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1097,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v3_tex_3 @ B @ A ) )
& ( v1_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tex_3) ).
thf(7706,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v3_tex_3 @ B @ A ) )
& ( v1_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(2148,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
| ( v4_pre_topc @ C @ A ) )
=> ( ( k3_tex_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tex_4) ).
thf(12842,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
| ( v4_pre_topc @ C @ A ) )
=> ( ( k3_tex_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148]) ).
thf(2005,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( ( ( ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ C )
= k1_xboole_0 )
| ( ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ B ) @ ( k13_borsuk_1 @ A @ B ) @ C )
= k1_xboole_0 ) )
=> ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_borsuk_1) ).
thf(12265,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( ( ( ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ C )
= k1_xboole_0 )
| ( ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ B ) @ ( k13_borsuk_1 @ A @ B ) @ C )
= k1_xboole_0 ) )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005]) ).
thf(1719,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ B @ D ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tops_3) ).
thf(11016,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ B @ D ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_partfun1) ).
thf(3262,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1577,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v2_pre_topc @ A ) )
=> ( v2_pre_topc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tex_2) ).
thf(10327,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v2_pre_topc @ A ) )
=> ( v2_pre_topc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(2111,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tops_1) ).
thf(12704,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ ( k4_relset_1 @ A @ B @ C ) )
& ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_funct_2) ).
thf(3289,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ ( k4_relset_1 @ A @ B @ C ) )
& ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1574,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( v3_pre_topc @ D @ B ) )
=> ( v3_pre_topc @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_borsuk_1) ).
thf(10321,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( v3_pre_topc @ D @ B ) )
=> ( v3_pre_topc @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(719,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tex_3) ).
thf(5608,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1564,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( B
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tex_4) ).
thf(10274,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( v1_tex_4 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( B
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( B
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) )
=> ( ( v1_tex_4 @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(1311,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc43_tex_2) ).
thf(8859,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
<=> ( ( k4_relset_1 @ B @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
thf(4269,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
=> ( ( k4_relset_1 @ B @ A @ C )
= B ) )
& ( ( ( k4_relset_1 @ B @ A @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
thf(4017,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(7910,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(1501,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tops_3) ).
thf(9974,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
<=> ( ( k5_relset_1 @ A @ B @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(2894,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
=> ( ( k5_relset_1 @ A @ B @ C )
= B ) )
& ( ( ( k5_relset_1 @ A @ B @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(89,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(2524,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(49,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(2376,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1296,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_tex_2) ).
thf(8807,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1900,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( r1_xboole_0 @ B @ C )
<=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tsep_1) ).
thf(11805,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
=> ( r1_connsp_1 @ A @ B @ C ) )
& ( ( r1_connsp_1 @ A @ B @ C )
=> ( r1_xboole_0 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900]) ).
thf(1242,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
=> ( ( r2_hidden @ C @ D )
=> ( D
= ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_borsuk_1) ).
thf(8495,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
=> ( ( r2_hidden @ C @ D )
=> ( D
= ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(311,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(3547,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1553,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_tops_1) ).
thf(10232,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(1343,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k2_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k2_borsuk_1 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k2_borsuk_1 @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_borsuk_1) ).
thf(9062,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k2_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k2_borsuk_1 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k2_borsuk_1 @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(2938,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1840,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tops_3) ).
thf(11566,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840]) ).
thf(302,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(3519,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(376,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(3945,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(1653,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( v3_tex_4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tex_4) ).
thf(10709,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( v3_tex_4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(964,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(6898,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(470,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ C @ D )
=> ( ( ( ( r4_tsep_1 @ A @ C @ B )
& ( r4_tsep_1 @ A @ D @ B ) )
=> ( r4_tsep_1 @ A @ ( k2_tsep_1 @ A @ C @ D ) @ B ) )
& ( ( ( r4_tsep_1 @ A @ B @ C )
& ( r4_tsep_1 @ A @ B @ D ) )
=> ( r4_tsep_1 @ A @ B @ ( k2_tsep_1 @ A @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tsep_1) ).
thf(4381,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ C @ D )
=> ( ( ( ( r4_tsep_1 @ A @ C @ B )
& ( r4_tsep_1 @ A @ D @ B ) )
=> ( r4_tsep_1 @ A @ ( k2_tsep_1 @ A @ C @ D ) @ B ) )
& ( ( ( r4_tsep_1 @ A @ B @ C )
& ( r4_tsep_1 @ A @ B @ D ) )
=> ( r4_tsep_1 @ A @ B @ ( k2_tsep_1 @ A @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(7472,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(3599,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1951,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( u1_struct_0 @ ( k3_t_0topsp @ A ) )
= ( k2_t_0topsp @ A ) )
& ( ( u1_pre_topc @ ( k3_t_0topsp @ A ) )
= ( a_1_0_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_t_0topsp) ).
thf(12028,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( u1_struct_0 @ ( k3_t_0topsp @ A ) )
= ( k2_t_0topsp @ A ) )
& ( ( u1_pre_topc @ ( k3_t_0topsp @ A ) )
= ( a_1_0_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(4041,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1406,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ D @ B )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tex_2) ).
thf(9418,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ D @ B )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ D @ B )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ D ) ) ) )
=> ( v4_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(1514,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v1_tops_2 @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) ) )
=> ( ( D = B )
=> ( v1_tops_2 @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tops_2) ).
thf(10068,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v1_tops_2 @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) ) )
=> ( ( D = B )
=> ( v1_tops_2 @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(1596,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( a_2_7_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_7_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tex_4) ).
thf(10425,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( a_2_7_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_7_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
= ( k5_relset_1 @ B @ A @ C ) )
& ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k4_relset_1 @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_relset_1) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
= ( k5_relset_1 @ B @ A @ C ) )
& ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k4_relset_1 @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1940,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tdlat_3 @ B )
=> ( v2_pre_topc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_tex_2) ).
thf(11983,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tdlat_3 @ B )
=> ( v2_pre_topc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940]) ).
thf(204,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( ( v4_tex_3 @ B @ A )
| ( v4_tex_3 @ C @ A ) )
& ~ ( r1_tsep_1 @ A @ B @ C )
& ~ ( v4_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tex_3) ).
thf(3070,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( ( v4_tex_3 @ B @ A )
| ( v4_tex_3 @ C @ A ) )
& ~ ( r1_tsep_1 @ A @ B @ C )
& ~ ( v4_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1135,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relset_1) ).
thf(7938,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
=> ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(446,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(4283,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(2171,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ B @ ( k15_borsuk_1 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B
!= ( k1_struct_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_borsuk_1) ).
thf(12914,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ B @ ( k15_borsuk_1 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B
!= ( k1_struct_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171]) ).
thf(1995,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( v4_pre_topc @ D @ B )
& ( v4_tops_1 @ D @ B ) )
=> ( v5_tops_1 @ D @ B ) )
& ( ( v5_tops_1 @ C @ A )
=> ( ( v4_pre_topc @ C @ A )
& ( v4_tops_1 @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_tops_1) ).
thf(12216,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( v4_pre_topc @ D @ B )
& ( v4_tops_1 @ D @ B ) )
=> ( v5_tops_1 @ D @ B ) )
& ( ( v5_tops_1 @ C @ A )
=> ( ( v4_pre_topc @ C @ A )
& ( v4_tops_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995]) ).
thf(1054,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc19_tex_2) ).
thf(7497,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
& ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_funcop_1) ).
thf(6881,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
& ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_2) ).
thf(6510,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(818,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tex_3) ).
thf(6108,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(3240,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_partfun1) ).
thf(2657,plain,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1854,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ C ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tex_4) ).
thf(11615,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ C ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k3_tarski @ D ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_borsuk_1) ).
thf(7233,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k3_tarski @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k3_tarski @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1984,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
=> ( v1_tops_2 @ ( k5_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tops_2) ).
thf(12170,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ B @ A )
=> ( v1_tops_2 @ ( k5_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984]) ).
thf(1928,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( m1_connsp_2 @ B @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
thf(11905,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( m1_connsp_2 @ B @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).
thf(1874,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
<=> ( v1_tops_2 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tops_2) ).
thf(11703,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tops_2 @ B @ A )
=> ( v1_tops_2 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v1_tops_2 @ ( k7_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v2_tops_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).
thf(451,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_partfun1) ).
thf(4309,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1238,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_tex_2) ).
thf(8470,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( B != k1_xboole_0 )
& ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) ) )
& ~ ( v2_funct_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_2) ).
thf(2188,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( B != k1_xboole_0 )
& ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) ) )
& ~ ( v2_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1813,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v5_tops_1 @ B @ A )
& ( v5_tops_1 @ C @ A ) )
=> ( v5_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_tops_1) ).
thf(11411,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v5_tops_1 @ B @ A )
& ( v5_tops_1 @ C @ A ) )
=> ( v5_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813]) ).
thf(1609,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_2 @ B @ A )
<=> ( ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tsp_2) ).
thf(10480,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_2 @ B @ A )
=> ( ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) ) )
& ( ( ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) )
=> ( v1_tsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k2_tarski @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(5962,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k2_tarski @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1174,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
<=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tsep_1) ).
thf(8124,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r1_tsep_1 @ A @ B @ C )
=> ( r3_tsep_1 @ A @ B @ C ) )
& ( ( r3_tsep_1 @ A @ B @ C )
=> ( r1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1456,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r1_tsep_1 @ A @ B @ C )
& ( r4_tsep_1 @ A @ B @ C ) )
<=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_tsep_1) ).
thf(9719,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( ( r1_tsep_1 @ A @ B @ C )
& ( r4_tsep_1 @ A @ B @ C ) )
=> ( r3_tsep_1 @ A @ B @ C ) )
& ( ( r3_tsep_1 @ A @ B @ C )
=> ( ( r1_tsep_1 @ A @ B @ C )
& ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(1524,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ( v2_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tops_3) ).
thf(10100,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ( v2_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v2_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(399,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( k2_tsep_1 @ A @ B @ C )
= ( k2_tsep_1 @ A @ C @ B ) ) )
& ( ( ( ~ ( r1_tsep_1 @ A @ B @ C )
& ~ ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D ) )
| ( ~ ( r1_tsep_1 @ A @ C @ D )
& ~ ( r1_tsep_1 @ A @ B @ ( k2_tsep_1 @ A @ C @ D ) ) ) )
=> ( ( k2_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D )
= ( k2_tsep_1 @ A @ B @ ( k2_tsep_1 @ A @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tsep_1) ).
thf(4032,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( k2_tsep_1 @ A @ B @ C )
= ( k2_tsep_1 @ A @ C @ B ) ) )
& ( ( ( ~ ( r1_tsep_1 @ A @ B @ C )
& ~ ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D ) )
| ( ~ ( r1_tsep_1 @ A @ C @ D )
& ~ ( r1_tsep_1 @ A @ B @ ( k2_tsep_1 @ A @ C @ D ) ) ) )
=> ( ( k2_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D )
= ( k2_tsep_1 @ A @ B @ ( k2_tsep_1 @ A @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1155,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tex_3) ).
thf(8027,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(2155,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k1_tex_4 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_tex_4) ).
thf(12862,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k1_tex_4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(5050,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(611,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ~ ( ~ ( r1_tsep_1 @ A @ B @ D )
& ~ ( r1_tsep_1 @ A @ D @ C )
& ~ ( ( ( k2_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D )
= ( k1_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ D ) @ ( k2_tsep_1 @ A @ C @ D ) ) )
& ( ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) )
= ( k1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ B ) @ ( k2_tsep_1 @ A @ D @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tsep_1) ).
thf(5099,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ~ ( ~ ( r1_tsep_1 @ A @ B @ D )
& ~ ( r1_tsep_1 @ A @ D @ C )
& ~ ( ( ( k2_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D )
= ( k1_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ D ) @ ( k2_tsep_1 @ A @ C @ D ) ) )
& ( ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) )
= ( k1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ B ) @ ( k2_tsep_1 @ A @ D @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(2169,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k3_pcomps_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) )
= ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k3_pcomps_1 @ A @ B ) @ ( k3_pcomps_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_pcomps_1) ).
thf(12909,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k3_pcomps_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) )
= ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k3_pcomps_1 @ A @ B ) @ ( k3_pcomps_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(7704,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1848,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
=> ( v2_tops_2 @ ( k5_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_tops_2) ).
thf(11598,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
=> ( v2_tops_2 @ ( k5_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).
thf(1605,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(10461,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( ( v3_membered @ A )
& ( v3_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc44_membered) ).
thf(3590,plain,
! [A: $i,B: $i] :
( ( ( v3_membered @ A )
& ( v3_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(514,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(4590,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(278,axiom,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3404,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1531,axiom,
! [A: $i] : ( l1_pre_topc @ ( k2_pcomps_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pcomps_1) ).
thf(10127,plain,
! [A: $i] : ( l1_pre_topc @ ( k2_pcomps_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(2137,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_tex_4) ).
thf(12787,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137]) ).
thf(751,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A )
& ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(5752,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A )
& ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1696,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_subset_1) ).
thf(10874,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(1947,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_4 @ B @ A )
<=> ( ( v1_tex_4 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tex_4) ).
thf(12011,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_4 @ B @ A )
=> ( ( v1_tex_4 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) ) )
& ( ( ( v1_tex_4 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ C @ A )
& ( r1_tarski @ B @ C ) )
=> ( B = C ) ) ) )
=> ( v3_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947]) ).
thf(942,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( v1_pre_topc @ ( k5_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k5_pcomps_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pcomps_1) ).
thf(6774,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( v1_pre_topc @ ( k5_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k5_pcomps_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(4946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(2160,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_tops_3) ).
thf(12877,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160]) ).
thf(1314,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ~ ( ~ ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ F @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_tsep_1) ).
thf(8872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ~ ( ~ ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ F @ A )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k10_relat_1 @ C @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_borsuk_1) ).
thf(3213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k10_relat_1 @ C @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(2058,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tex_2) ).
thf(12473,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_borsuk_1) ).
thf(5471,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(2115,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( m1_subset_1 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_borsuk_1) ).
thf(12716,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( m1_subset_1 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115]) ).
thf(1047,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tsep_1) ).
thf(7465,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1910,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tops_2) ).
thf(11841,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910]) ).
thf(713,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_pre_topc) ).
thf(5578,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1161,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tsep_1) ).
thf(8064,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
=> ( ( ( r2_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A ) ) ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(234,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( l1_pre_topc @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( v3_tops_2 @ D @ A @ B )
& ( v3_tops_2 @ E @ B @ C ) )
=> ( v3_tops_2 @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tops_2) ).
thf(3223,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( l1_pre_topc @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( v3_tops_2 @ D @ A @ B )
& ( v3_tops_2 @ E @ B @ C ) )
=> ( v3_tops_2 @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1512,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( m2_connsp_2 @ ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ ( k1_struct_0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_borsuk_1) ).
thf(10044,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( m2_connsp_2 @ ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ ( k1_struct_0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(793,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_2 @ A @ B @ C )
=> ( ( v3_tex_3 @ B @ A )
<=> ( v1_tex_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tex_3) ).
thf(5965,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_2 @ A @ B @ C )
=> ( ( ( v3_tex_3 @ B @ A )
=> ( v1_tex_3 @ C @ A ) )
& ( ( v1_tex_3 @ C @ A )
=> ( v3_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(5185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1905,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v1_tops_1 @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tops_3) ).
thf(11819,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v1_tops_1 @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905]) ).
thf(705,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_tex_3) ).
thf(5546,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(194,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(3023,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(8534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1492,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tsep_1) ).
thf(9935,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(1635,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ( v3_compts_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_pcomps_1) ).
thf(10611,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A )
& ( v3_compts_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(1366,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
& ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ D ) )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( E
= ( k12_mcart_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ G ) )
& ( v3_pre_topc @ F @ A )
& ( v3_pre_topc @ G @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_borsuk_1) ).
thf(9210,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
& ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ D ) )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( E
= ( k12_mcart_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ G ) )
& ( v3_pre_topc @ F @ A )
& ( v3_pre_topc @ G @ B ) ) ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
& ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ D ) )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( E
= ( k12_mcart_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ G ) )
& ( v3_pre_topc @ F @ A )
& ( v3_pre_topc @ G @ B ) ) ) ) ) )
=> ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(712,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_tex_3) ).
thf(5567,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(417,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ D )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( r3_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_tsep_1) ).
thf(4096,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ D )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( r3_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( C
= ( k3_binop_1 @ A @ B ) )
<=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_binop_1) ).
thf(4837,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( C
= ( k3_binop_1 @ A @ B ) )
=> ( r3_binop_1 @ A @ C @ B ) )
& ( ( r3_binop_1 @ A @ C @ B )
=> ( C
= ( k3_binop_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( v1_partfun1 @ C @ A @ B )
<=> ( ( k4_relset_1 @ A @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_partfun1) ).
thf(4645,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( v1_partfun1 @ C @ A @ B )
=> ( ( k4_relset_1 @ A @ B @ C )
= A ) )
& ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1731,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
=> ( m2_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_borsuk_1) ).
thf(11060,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
=> ( m2_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(1672,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ C @ A @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ B )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_connsp_2) ).
thf(10770,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( m1_connsp_2 @ C @ A @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( m1_connsp_2 @ D @ A @ B )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(326,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( l1_pre_topc @ ( k5_pcomps_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_pcomps_1) ).
thf(3651,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( l1_pre_topc @ ( k5_pcomps_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1200,axiom,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(8249,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1276,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc29_tex_3) ).
thf(8665,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(657,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( k1_funct_1 @ ( k12_borsuk_1 @ A @ B ) @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k1_funct_1 @ ( k13_borsuk_1 @ A @ B ) @ k1_xboole_0 )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_borsuk_1) ).
thf(5282,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( k1_funct_1 @ ( k12_borsuk_1 @ A @ B ) @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k1_funct_1 @ ( k13_borsuk_1 @ A @ B ) @ k1_xboole_0 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
=> ( r1_partfun1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(4218,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
=> ( r1_partfun1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(2935,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(2074,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v1_tops_3 @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tops_3) ).
thf(12524,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v1_tops_3 @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074]) ).
thf(1583,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(10348,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(481,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(4413,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(3594,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1208,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_tex_3) ).
thf(8300,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1424,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k1_pre_topc @ A ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k2_pre_topc @ A ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k2_pre_topc @ A ) )
=> ( B
= ( k1_pre_topc @ A ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( u1_struct_0 @ A ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( u1_struct_0 @ A ) )
=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tops_3) ).
thf(9538,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k1_pre_topc @ A ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k2_pre_topc @ A ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k2_pre_topc @ A ) )
=> ( B
= ( k1_pre_topc @ A ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( u1_struct_0 @ A ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( u1_struct_0 @ A ) )
=> ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(1465,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ B @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
<=> ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relset_1) ).
thf(9776,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ B @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ( ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
=> ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) )
& ( ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(2126,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v4_tex_4 @ B @ A )
<=> ( v3_tex_4 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tex_4) ).
thf(12748,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v4_tex_4 @ B @ A )
=> ( v3_tex_4 @ C @ A ) )
& ( ( v3_tex_4 @ C @ A )
=> ( v4_tex_4 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126]) ).
thf(135,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ ( k5_funcop_1 @ B @ D @ A ) ) )
=> ( ( k1_funct_1 @ ( k5_funcop_1 @ B @ D @ A ) @ C )
= ( k1_binop_1 @ B @ D @ ( k1_funct_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funcop_1) ).
thf(2753,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ ( k5_funcop_1 @ B @ D @ A ) ) )
=> ( ( k1_funct_1 @ ( k5_funcop_1 @ B @ D @ A ) @ C )
= ( k1_binop_1 @ B @ D @ ( k1_funct_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(2176,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tops_3) ).
thf(12936,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2176]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v4_membered @ B ) )
=> ( v4_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_membered) ).
thf(5207,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v4_membered @ B ) )
=> ( v4_membered @ ( k1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(5314,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ B @ C ) ) @ A )
= ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ B @ ( k9_funct_3 @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_borsuk_1) ).
thf(3487,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ B @ C ) ) @ A )
= ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ B @ ( k9_funct_3 @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(704,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v5_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc39_tex_2) ).
thf(5539,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v5_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(6636,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1977,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) )
& ( m1_pre_topc @ ( k6_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_tex_4) ).
thf(12146,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) )
& ( m1_pre_topc @ ( k6_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(6123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(61,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_2 @ A )
& ( v8_relat_2 @ A ) )
=> ( v1_relat_2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_2) ).
thf(2425,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_2 @ A )
& ( v8_relat_2 @ A ) )
=> ( v1_relat_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1380,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_2 @ A @ B @ C )
=> ( ( v2_tex_2 @ B @ A )
& ( v2_tex_2 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tex_3) ).
thf(9290,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r4_tsep_2 @ A @ B @ C )
=> ( ( v2_tex_2 @ B @ A )
& ( v2_tex_2 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(2144,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( m1_pre_topc @ ( k1_tex_2 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tex_2) ).
thf(12825,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( m1_pre_topc @ ( k1_tex_2 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144]) ).
thf(2010,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( m1_subset_1 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tsep_1) ).
thf(12280,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( m1_subset_1 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010]) ).
thf(1631,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(10596,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_partfun1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_2) ).
thf(5784,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_partfun1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(1855,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
& ( v1_tsp_1 @ C @ A ) )
=> ( ( ~ ( v3_pre_topc @ B @ A )
& ~ ( v3_pre_topc @ C @ A ) )
| ( v1_tsp_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tsp_1) ).
thf(11618,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
& ( v1_tsp_1 @ C @ A ) )
=> ( ( ~ ( v3_pre_topc @ B @ A )
& ~ ( v3_pre_topc @ C @ A ) )
| ( v1_tsp_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(6372,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( r1_tarski @ ( k2_tarski @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1394,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( r1_borsuk_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tex_2) ).
thf(9354,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( r1_borsuk_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(3302,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1224,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
<=> ( ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ B )
& ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tops_1) ).
thf(8387,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_tops_1 @ B @ A )
=> ( ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ B )
& ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) )
& ( ( ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ B )
& ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) )
=> ( v4_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(2009,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_pre_topc @ ( k5_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tex_4) ).
thf(12278,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_pre_topc @ ( k5_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(4887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(265,axiom,
( ~ ( v1_xboole_0 @ k1_numbers )
& ( v1_membered @ k1_numbers )
& ( v2_membered @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_membered) ).
thf(3355,plain,
( ~ ( v1_xboole_0 @ k1_numbers )
& ( v1_membered @ k1_numbers )
& ( v2_membered @ k1_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1661,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_tops_1 @ ( k1_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tops_3) ).
thf(10741,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_tops_1 @ ( k1_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(2157,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k3_pcomps_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pcomps_1) ).
thf(12867,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k3_pcomps_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157]) ).
thf(1828,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ~ ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ~ ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tsp_1) ).
thf(11525,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ~ ( v1_tsp_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ~ ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(842,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_t_0topsp @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_pre_topc @ A @ B @ C @ ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ D ) )
= ( k1_struct_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_t_0topsp) ).
thf(6261,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_t_0topsp @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_pre_topc @ A @ B @ C @ ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ D ) )
= ( k1_struct_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(1419,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_tops_3) ).
thf(9483,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) )
=> ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(1199,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v5_pre_topc @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_pre_topc @ D @ B )
=> ( v4_pre_topc @ ( k5_pre_topc @ A @ B @ C @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_pre_topc) ).
thf(8244,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_pre_topc @ D @ B )
=> ( v4_pre_topc @ ( k5_pre_topc @ A @ B @ C @ D ) @ A ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_pre_topc @ D @ B )
=> ( v4_pre_topc @ ( k5_pre_topc @ A @ B @ C @ D ) @ A ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(2142,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tops_1) ).
thf(12814,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142]) ).
thf(1534,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m2_connsp_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_connsp_2) ).
thf(10140,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m2_connsp_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(1499,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(9967,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(2081,axiom,
! [A: $i] : ( m1_subset_1 @ ( k1_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(12547,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081]) ).
thf(1051,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc48_tex_2) ).
thf(7482,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(3532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(892,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(6525,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(808,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v5_compts_1 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( C
!= ( k2_pre_topc @ A ) )
& ( r1_tarski @ B @ C )
& ( v4_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ ( k6_pre_topc @ A @ D ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_connsp_2) ).
thf(6048,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v5_compts_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( C
!= ( k2_pre_topc @ A ) )
& ( r1_tarski @ B @ C )
& ( v4_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ ( k6_pre_topc @ A @ D ) @ C ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( C
!= ( k2_pre_topc @ A ) )
& ( r1_tarski @ B @ C )
& ( v4_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ ( k6_pre_topc @ A @ D ) @ C ) ) ) ) ) )
=> ( v5_compts_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(901,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v5_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc20_tex_2) ).
thf(6585,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v5_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_binop_1) ).
thf(2361,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ( r1_binop_1 @ A @ C @ B ) )
& ( ( r1_binop_1 @ A @ C @ B )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(5870,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1228,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k3_subset_1 @ A @ ( k5_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
thf(8408,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k3_subset_1 @ A @ ( k5_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(545,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( ( r1_xboole_0 @ D @ C )
| ( r1_tarski @ D @ C ) ) ) )
=> ( C
= ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k2_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_borsuk_1) ).
thf(4704,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( ( r1_xboole_0 @ D @ C )
| ( r1_tarski @ D @ C ) ) ) )
=> ( C
= ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k2_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(1602,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_tops_1 @ B @ A )
<=> ( v5_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_tops_1) ).
thf(10448,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v6_tops_1 @ B @ A )
=> ( v5_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v5_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v6_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(465,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_relat_1) ).
thf(4369,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1998,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_1_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tex_4) ).
thf(12227,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_1_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998]) ).
thf(1329,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc17_tex_2) ).
thf(8970,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(680,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(5381,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(6144,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(7529,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(1536,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v4_tex_2 @ C @ A )
<=> ( v5_tex_2 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tex_2) ).
thf(10151,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v4_tex_2 @ C @ A )
=> ( v5_tex_2 @ B @ A ) )
& ( ( v5_tex_2 @ B @ A )
=> ( v4_tex_2 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(1621,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(10532,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(2095,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_borsuk_1 @ A @ B @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_borsuk_1) ).
thf(12651,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_borsuk_1 @ A @ B @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095]) ).
thf(1084,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tex_3) ).
thf(7643,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v4_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1747,axiom,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(11117,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(2100,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ ( k3_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tex_4) ).
thf(12668,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ ( k3_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100]) ).
thf(1385,axiom,
( ( v1_funct_1 @ k3_metric_1 )
& ( v1_funct_2 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers )
& ( m2_relset_1 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_metric_1) ).
thf(9312,plain,
( ( v1_funct_1 @ k3_metric_1 )
& ( v1_funct_2 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers )
& ( m2_relset_1 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v2_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A )
& ( m1_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k20_borsuk_1) ).
thf(6920,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v2_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A )
& ( m1_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C )
& ( v2_funct_1 @ E ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ D )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_2) ).
thf(2214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C )
& ( v2_funct_1 @ E ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ D )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(60,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_membered @ A ) )
=> ? [B: $i] :
( ( v4_ordinal2 @ B )
& ( r2_hidden @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_membered) ).
thf(2422,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_membered @ A ) )
=> ? [B: $i] :
( ( v4_ordinal2 @ B )
& ( r2_hidden @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k5_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(7907,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k5_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1178,axiom,
! [A: $i] :
( ( v1_funct_1 @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(8135,plain,
! [A: $i] :
( ( ( v1_funct_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) )
=> ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1396,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k2_pre_topc @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pre_topc) ).
thf(9377,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k2_pre_topc @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) )
& ( v1_borsuk_1 @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) )
& ( m1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k21_borsuk_1) ).
thf(6147,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) )
& ( v1_borsuk_1 @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) )
& ( m1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(3957,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(6217,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(6500,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1198,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc41_tex_2) ).
thf(8237,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(2906,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(7379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
& ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(834,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_tex_2) ).
thf(6197,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k2_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k2_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k2_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k2_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tsp_2) ).
thf(7607,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k2_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k2_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k2_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k2_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1172,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tops_1) ).
thf(8120,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ C )
<=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(5303,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1312,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(8868,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(1699,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_pcomps_1 @ A @ B ) @ ( k3_pcomps_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pcomps_1) ).
thf(10898,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_pcomps_1 @ A @ B ) @ ( k3_pcomps_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_2) ).
thf(3270,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1280,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).
thf(8693,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_2) ).
thf(2299,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1800,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(11355,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).
thf(1488,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tex_2) ).
thf(9920,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1509,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tops_1) ).
thf(10037,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(1211,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ B @ C )
& ( v5_tex_2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tex_2) ).
thf(8313,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ B @ C )
& ( v5_tex_2 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(115,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(2669,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
<=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(5222,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) )
& ( ( r1_tarski @ B @ C )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(2096,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ D )
& ( r2_tsep_1 @ A @ C @ D ) )
=> ( r2_tsep_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tsep_1) ).
thf(12656,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ D )
& ( r2_tsep_1 @ A @ C @ D ) )
=> ( r2_tsep_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).
thf(2839,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(2079,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_tex_2 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_pre_topc @ B @ ( k1_struct_0 @ B @ D ) ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_tex_2) ).
thf(12537,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_tex_2 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_pre_topc @ B @ ( k1_struct_0 @ B @ D ) ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_pre_topc @ B @ ( k1_struct_0 @ B @ D ) ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_tex_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079]) ).
thf(176,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(2945,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1796,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v2_tops_1 @ B @ A ) )
=> ( ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(11338,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v2_tops_1 @ B @ A ) )
=> ( ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(1457,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tsep_1) ).
thf(9723,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( v3_pre_topc @ F @ A ) ) ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funcop_1) ).
thf(4213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(4073,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(609,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
=> ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funcop_1) ).
thf(5093,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
=> ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(703,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_tex_3 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc28_tex_3) ).
thf(5531,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_tex_3 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1974,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( C
= ( k7_tex_4 @ A @ B ) )
<=> ( ( u1_struct_0 @ C )
= ( k3_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_tex_4) ).
thf(12136,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( C
= ( k7_tex_4 @ A @ B ) )
=> ( ( u1_struct_0 @ C )
= ( k3_tex_4 @ A @ B ) ) )
& ( ( ( u1_struct_0 @ C )
= ( k3_tex_4 @ A @ B ) )
=> ( C
= ( k7_tex_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974]) ).
thf(1568,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( v1_tops_1 @ C @ A )
& ( v1_tops_1 @ E @ B ) )
<=> ( v1_tops_1 @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_tops_3) ).
thf(10296,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( ( v1_tops_1 @ C @ A )
& ( v1_tops_1 @ E @ B ) )
=> ( v1_tops_1 @ D @ A ) )
& ( ( v1_tops_1 @ D @ A )
=> ( ( v1_tops_1 @ C @ A )
& ( v1_tops_1 @ E @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(4374,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(1258,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v2_tops_1 @ ( k1_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tops_3) ).
thf(8561,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v2_tops_1 @ ( k1_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(2166,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v3_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( B
= ( k2_tex_4 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_tex_4) ).
thf(12894,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v3_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( B
= ( k2_tex_4 @ A @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( B
= ( k2_tex_4 @ A @ C ) ) ) )
=> ( v3_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166]) ).
thf(934,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tex_2) ).
thf(6737,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1829,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ C @ A )
=> ( v1_tops_2 @ ( k1_tops_2 @ A @ B @ C ) @ ( k3_pre_topc @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tops_2) ).
thf(11531,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_tops_2 @ C @ A )
=> ( v1_tops_2 @ ( k1_tops_2 @ A @ B @ C ) @ ( k3_pre_topc @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).
thf(1877,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tex_4 @ B @ A )
=> ( ( ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B )
= k1_xboole_0 )
| ( v1_tex_4 @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tex_4) ).
thf(11718,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tex_4 @ B @ A )
=> ( ( ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B )
= k1_xboole_0 )
| ( v1_tex_4 @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).
thf(1027,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(7307,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_binop_1) ).
thf(2197,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ( r2_binop_1 @ A @ C @ B ) )
& ( ( r2_binop_1 @ A @ C @ B )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2033,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D )
= ( k1_tsep_1 @ A @ B @ ( k1_tsep_1 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tsep_1) ).
thf(12369,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D )
= ( k1_tsep_1 @ A @ B @ ( k1_tsep_1 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).
thf(1454,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(9713,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(2056,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tex_4) ).
thf(12464,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(4203,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( r1_partfun1 @ C @ D )
<=> ! [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_2) ).
thf(2812,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( r1_partfun1 @ C @ D )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) )
& ( ! [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1448,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(9655,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(24,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ E ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
=> ( D
= ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funcop_1) ).
thf(2267,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ E ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
=> ( D
= ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1686,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v1_tops_3 @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tops_3) ).
thf(10825,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v1_tops_3 @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(954,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6847,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1645,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_tex_4) ).
thf(10645,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(1339,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_tsep_1) ).
thf(9042,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(814,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v5_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tex_3) ).
thf(6087,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v5_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= A )
& ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funcop_1) ).
thf(4430,plain,
! [A: $i,B: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= A )
& ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1272,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(8633,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(785,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tsep_1) ).
thf(5920,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A ) ) )
=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(2150,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ D @ C )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v2_tops_1 @ C @ A ) )
=> ( v2_tops_1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_tops_3) ).
thf(12850,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ D @ C )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v2_tops_1 @ C @ A ) )
=> ( v2_tops_1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150]) ).
thf(1969,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k3_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tex_4) ).
thf(12114,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k3_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969]) ).
thf(1560,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tops_1) ).
thf(10253,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(1001,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( v5_pre_topc @ C @ B @ A ) ) )
=> ( v2_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tex_2) ).
thf(7113,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( v5_pre_topc @ C @ B @ A ) ) )
=> ( v2_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(3668,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1182,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_pre_topc @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tsep_1) ).
thf(8156,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_pre_topc @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(955,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_pre_topc @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tops_2) ).
thf(6849,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) )
=> ( v3_pre_topc @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1275,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ( r3_tsep_1 @ A @ B @ D )
& ( r3_tsep_1 @ A @ C @ D ) )
<=> ( r3_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tsep_1) ).
thf(8661,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ( ( r3_tsep_1 @ A @ B @ D )
& ( r3_tsep_1 @ A @ C @ D ) )
=> ( r3_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D ) )
& ( ( r3_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ C ) @ D )
=> ( ( r3_tsep_1 @ A @ B @ D )
& ( r3_tsep_1 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(205,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funcop_1) ).
thf(3073,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1168,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k17_borsuk_1 @ A @ B )
= ( k2_borsuk_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_borsuk_1) ).
thf(8103,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k17_borsuk_1 @ A @ B )
= ( k2_borsuk_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1770,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v3_tex_4 @ C @ A ) )
=> ( v3_tex_4 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tex_4) ).
thf(11205,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v3_tex_4 @ C @ A ) )
=> ( v3_tex_4 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(1069,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( v4_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tex_2) ).
thf(7566,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( v4_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(22,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_2 @ A )
=> ( v3_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_2) ).
thf(2261,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_2 @ A )
=> ( v3_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1764,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ B )
= ( k3_tarski @ ( a_2_6_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_tex_4) ).
thf(11188,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ B )
= ( k3_tarski @ ( a_2_6_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(2076,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( C = D )
=> ( r1_tarski @ ( k1_connsp_1 @ B @ D ) @ ( k1_connsp_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_connsp_2) ).
thf(12528,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( C = D )
=> ( r1_tarski @ ( k1_connsp_1 @ B @ D ) @ ( k1_connsp_1 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(4264,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1117,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(7820,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(978,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tex_2) ).
thf(6974,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= C ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1125,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tsp_1) ).
thf(7892,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(716,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v3_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_tex_3) ).
thf(5599,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v3_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1376,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v1_tdlat_3 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc25_tex_2) ).
thf(9263,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v1_tdlat_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_partfun1) ).
thf(2446,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1779,axiom,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(11233,plain,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(1967,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(12111,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967]) ).
thf(989,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_pre_topc) ).
thf(7033,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(2127,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_t_0topsp) ).
thf(12755,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2127]) ).
thf(1089,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(7664,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1935,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ C )
& ( r1_xboole_0 @ E @ B )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tsep_1) ).
thf(11964,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ C )
& ( r1_xboole_0 @ E @ B )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ C )
& ( r1_xboole_0 @ E @ B )
& ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A ) ) )
=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935]) ).
thf(1066,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tex_2) ).
thf(7551,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(6414,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(3192,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(921,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_pre_topc) ).
thf(6678,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_partfun1) ).
thf(3006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k1_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k1_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k1_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k1_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tsp_2) ).
thf(6080,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k1_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k1_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k1_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k1_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1221,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(8372,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(1331,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_membered) ).
thf(8998,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(693,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_tex_3) ).
thf(5466,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1293,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(8782,plain,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(1610,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_3) ).
thf(10489,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(2119,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v1_tops_2 @ C @ A ) )
=> ( v1_tops_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tops_2) ).
thf(12727,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v1_tops_2 @ C @ A ) )
=> ( v1_tops_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119]) ).
thf(1594,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v2_pcomps_1 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_pre_topc @ A @ B )
& ( v1_tops_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_2 @ C @ A )
& ( r1_pre_topc @ A @ C )
& ( r1_setfam_1 @ C @ B )
& ( v1_pcomps_1 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_pcomps_1) ).
thf(10412,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ( v2_pcomps_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_pre_topc @ A @ B )
& ( v1_tops_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_2 @ C @ A )
& ( r1_pre_topc @ A @ C )
& ( r1_setfam_1 @ C @ B )
& ( v1_pcomps_1 @ C @ A ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_pre_topc @ A @ B )
& ( v1_tops_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_2 @ C @ A )
& ( r1_pre_topc @ A @ C )
& ( r1_setfam_1 @ C @ B )
& ( v1_pcomps_1 @ C @ A ) ) ) ) )
=> ( v2_pcomps_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(1944,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
<=> ( v2_tex_2 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tex_2) ).
thf(12000,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v2_tex_2 @ B @ A ) )
& ( ( v2_tex_2 @ B @ A )
=> ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944]) ).
thf(880,axiom,
! [A: $i,B: $i] :
( ( B
= ( k3_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(6446,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k3_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_2) ).
thf(2553,plain,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(5007,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(1889,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_pcomps_1 @ B @ A )
& ( v2_tops_2 @ B @ A ) )
=> ( v4_pre_topc @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_pcomps_1) ).
thf(11761,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_pcomps_1 @ B @ A )
& ( v2_tops_2 @ B @ A ) )
=> ( v4_pre_topc @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_partfun1) ).
thf(2329,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1230,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tex_4) ).
thf(8413,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tdlat_3 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1806,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k4_tex_4 @ A @ C ) )
= ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tsp_2) ).
thf(11375,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k4_tex_4 @ A @ C ) )
= ( k1_struct_0 @ A @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k4_tex_4 @ A @ C ) )
= ( k1_struct_0 @ A @ C ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).
thf(167,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(2911,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funcop_1) ).
thf(4554,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1190,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( C
= ( k3_pre_topc @ A @ B ) )
<=> ( ( k2_pre_topc @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_pre_topc) ).
thf(8198,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( C
= ( k3_pre_topc @ A @ B ) )
=> ( ( k2_pre_topc @ C )
= B ) )
& ( ( ( k2_pre_topc @ C )
= B )
=> ( C
= ( k3_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(801,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(5987,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1790,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(11310,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).
thf(2046,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k1_setfam_1 @ ( a_2_1_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tex_4) ).
thf(12432,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k1_setfam_1 @ ( a_2_1_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(2835,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(828,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc14_tex_2) ).
thf(6151,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(888,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_borsuk_1) ).
thf(6504,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1363,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ E ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
| ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_borsuk_1) ).
thf(9197,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ E ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
| ( D = E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(1037,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k16_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_borsuk_1) ).
thf(7366,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k16_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ D )
= B )
& ( ( k2_relat_1 @ E )
= C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_2) ).
thf(4196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ D )
= B )
& ( ( k2_relat_1 @ E )
= C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(309,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(3539,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1762,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v3_pre_topc @ D @ B )
<=> ( v3_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tsep_1) ).
thf(11173,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v3_pre_topc @ D @ B )
=> ( v3_pre_topc @ C @ A ) )
& ( ( v3_pre_topc @ C @ A )
=> ( v3_pre_topc @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(1439,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).
thf(9610,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k4_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k4_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k4_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k4_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tsp_2) ).
thf(6345,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k4_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k4_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k4_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k4_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1650,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v2_tops_2 @ ( k3_pcomps_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pcomps_1) ).
thf(10660,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v2_tops_2 @ ( k3_pcomps_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(548,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(4720,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1233,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tdlat_3 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc26_tex_2) ).
thf(8440,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tdlat_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(651,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(5254,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(753,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) )
& ( v2_tex_2 @ B @ A ) )
=> ( v2_tex_2 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_tex_2) ).
thf(5775,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) )
& ( v2_tex_2 @ B @ A ) )
=> ( v2_tex_2 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(437,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k1_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(4232,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k1_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(988,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( a_2_5_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_5_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_tex_4) ).
thf(7030,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( a_2_5_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_5_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1417,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(9478,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(127,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_relat_1) ).
thf(2725,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1724,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ C ) )
<=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tex_4) ).
thf(11041,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k2_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ C ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) )
& ( ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
=> ( ( k2_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(2078,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tex_4) ).
thf(12534,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078]) ).
thf(2134,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k6_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_tex_4) ).
thf(12779,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k6_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134]) ).
thf(1284,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(8719,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(1616,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k3_tarski @ ( a_2_2_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_tex_4) ).
thf(10514,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k3_tarski @ ( a_2_2_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(1300,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(8821,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1878,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v1_tex_4 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tex_4) ).
thf(11721,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v1_tex_4 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v1_tex_4 @ C @ A ) ) )
=> ( v2_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).
thf(1372,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r2_hidden @ A @ B )
& ~ ( r2_hidden @ C @ B )
& ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(9249,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r2_hidden @ A @ B )
& ~ ( r2_hidden @ C @ B )
& ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(5516,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1783,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r1_xboole_0 @ ( k2_tex_4 @ A @ C ) @ ( k3_tex_4 @ A @ B ) )
& ( r1_xboole_0 @ ( k2_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tex_4) ).
thf(11245,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r1_xboole_0 @ ( k2_tex_4 @ A @ C ) @ ( k3_tex_4 @ A @ B ) )
& ( r1_xboole_0 @ ( k2_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(650,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) @ ( k12_borsuk_1 @ A @ B ) @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ~ ( ( r2_hidden @ E @ C )
& ( D
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ A ) @ ( k9_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_borsuk_1) ).
thf(5248,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k2_funct_2 @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) @ ( k12_borsuk_1 @ A @ B ) @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ~ ( ( r2_hidden @ E @ C )
& ( D
= ( k2_funct_2 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ A ) @ ( k9_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(351,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(3806,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1921,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k3_t_0topsp @ A ) )
& ( v2_pre_topc @ ( k3_t_0topsp @ A ) )
& ( v2_t_0topsp @ ( k3_t_0topsp @ A ) )
& ( l1_pre_topc @ ( k3_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_t_0topsp) ).
thf(11874,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k3_t_0topsp @ A ) )
& ( v2_pre_topc @ ( k3_t_0topsp @ A ) )
& ( v2_t_0topsp @ ( k3_t_0topsp @ A ) )
& ( l1_pre_topc @ ( k3_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921]) ).
thf(1745,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tops_3) ).
thf(11113,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(3159,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1697,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_tops_1) ).
thf(10893,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(796,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tex_3) ).
thf(5976,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1254,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ( ( v1_borsuk_1 @ B @ A )
| ( v1_borsuk_1 @ C @ A ) )
=> ( v2_t_0topsp @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tsp_1) ).
thf(8541,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ( ( v1_borsuk_1 @ B @ A )
| ( v1_borsuk_1 @ C @ A ) )
=> ( v2_t_0topsp @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(2066,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tdlat_3 @ B )
=> ( v2_pre_topc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_tex_2) ).
thf(12497,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tdlat_3 @ B )
=> ( v2_pre_topc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066]) ).
thf(1351,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tdlat_3 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tex_2) ).
thf(9106,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tdlat_3 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(20,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_partfun1) ).
thf(2244,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1527,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tops_1) ).
thf(10108,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(583,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(4918,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(2130,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v4_pre_topc @ C @ A ) )
=> ( C
= ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tops_3) ).
thf(12765,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v4_pre_topc @ C @ A ) )
=> ( C
= ( u1_struct_0 @ A ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v4_pre_topc @ C @ A ) )
=> ( C
= ( u1_struct_0 @ A ) ) ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130]) ).
thf(267,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( l1_struct_0 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ D )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ D )
& ( ( k1_relat_1 @ E )
= ( k2_pre_topc @ B ) )
& ( ( k2_relat_1 @ E )
= ( k2_pre_topc @ C ) )
& ( v2_funct_1 @ E ) )
=> ( ( k2_tops_2 @ A @ C @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
= ( k7_funct_2 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( k2_tops_2 @ B @ C @ E ) @ ( k2_tops_2 @ A @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tops_2) ).
thf(3363,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( l1_struct_0 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ D )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ D )
& ( ( k1_relat_1 @ E )
= ( k2_pre_topc @ B ) )
& ( ( k2_relat_1 @ E )
= ( k2_pre_topc @ C ) )
& ( v2_funct_1 @ E ) )
=> ( ( k2_tops_2 @ A @ C @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
= ( k7_funct_2 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( k2_tops_2 @ B @ C @ E ) @ ( k2_tops_2 @ A @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1850,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) )
= ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tops_3) ).
thf(11605,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) )
= ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).
thf(2094,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( C
= ( k6_tex_4 @ A @ B ) )
<=> ( ( u1_struct_0 @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_tex_4) ).
thf(12644,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( C
= ( k6_tex_4 @ A @ B ) )
=> ( ( u1_struct_0 @ C )
= B ) )
& ( ( ( u1_struct_0 @ C )
= B )
=> ( C
= ( k6_tex_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094]) ).
thf(1896,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tops_3) ).
thf(11781,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896]) ).
thf(1391,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(9345,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
thf(3178,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(3512,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k3_t_0topsp @ A )
= ( k16_borsuk_1 @ A @ ( k2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_t_0topsp) ).
thf(12224,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k3_t_0topsp @ A )
= ( k16_borsuk_1 @ A @ ( k2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(8291,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2999,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(737,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_tex_4 @ A @ B )
= ( k3_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_tex_4) ).
thf(5693,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_tex_4 @ A @ B )
= ( k3_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k1_setfam_1 @ ( a_2_9_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1459,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ( v3_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tex_3) ).
thf(9740,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ( v3_pre_topc @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(262,axiom,
~ ( v1_xboole_0 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_numbers) ).
thf(3348,plain,
~ ( v1_xboole_0 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1131,axiom,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(7916,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t163_relat_1) ).
thf(2207,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1827,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C
!= ( u1_struct_0 @ A ) )
& ( v4_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ D )
& ( D
!= ( u1_struct_0 @ A ) )
& ( v4_pre_topc @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_tops_3) ).
thf(11507,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C
!= ( u1_struct_0 @ A ) )
& ( v4_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ D )
& ( D
!= ( u1_struct_0 @ A ) )
& ( v4_pre_topc @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C
!= ( u1_struct_0 @ A ) )
& ( v4_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ D )
& ( D
!= ( u1_struct_0 @ A ) )
& ( v4_pre_topc @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( u1_struct_0 @ A ) ) ) ) ) )
=> ( v1_tops_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(5139,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(371,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(3908,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(927,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(6698,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(429,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(4209,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(495,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(4481,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(945,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(6785,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(932,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tsep_1) ).
thf(6730,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
& ( r3_tsep_1 @ A @ B @ C ) )
=> ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(882,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ~ ( ( v1_tops_2 @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_2 @ D @ A )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( E
= ( k2_pre_topc @ B ) )
=> ( C
= ( k1_tops_2 @ A @ E @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tops_2) ).
thf(6476,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ~ ( ( v1_tops_2 @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_2 @ D @ A )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( E
= ( k2_pre_topc @ B ) )
=> ( C
= ( k1_tops_2 @ A @ E @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1669,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_tex_4) ).
thf(10762,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(1958,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A ) )
=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_tops_1) ).
thf(12060,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A ) )
=> ( C = k1_xboole_0 ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A ) )
=> ( C = k1_xboole_0 ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958]) ).
thf(413,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_eqrel_1 @ B @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_setfam_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_borsuk_1) ).
thf(4084,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_eqrel_1 @ B @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_setfam_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1332,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(9001,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(992,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(7049,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(3490,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(5619,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(4741,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_2) ).
thf(4136,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(7526,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1475,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tex_2) ).
thf(9826,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
& ( r2_hidden @ B @ C )
& ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(8116,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
& ( r2_hidden @ B @ C )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1245,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(8505,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(1113,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_pre_topc @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_pre_topc) ).
thf(7773,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) )
=> ( v4_pre_topc @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(2036,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tops_2 @ B @ A )
& ( v1_finset_1 @ B ) )
=> ( v3_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tops_2) ).
thf(12377,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v1_tops_2 @ B @ A )
& ( v1_finset_1 @ B ) )
=> ( v3_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v2_struct_0 @ ( g2_struct_0 @ A @ B ) )
& ( l2_struct_0 @ ( g2_struct_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_struct_0) ).
thf(5358,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v2_struct_0 @ ( g2_struct_0 @ A @ B ) )
& ( l2_struct_0 @ ( g2_struct_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(5003,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(913,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tex_3) ).
thf(6641,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(2163,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tops_1) ).
thf(12886,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163]) ).
thf(368,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(3881,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(730,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(5661,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(940,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(6768,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(692,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_tsp_1) ).
thf(5463,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1759,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v1_tsp_1 @ C @ A )
<=> ( v2_t_0topsp @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_tsp_1) ).
thf(11161,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v1_tsp_1 @ C @ A )
=> ( v2_t_0topsp @ B ) )
& ( ( v2_t_0topsp @ B )
=> ( v1_tsp_1 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(460,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k5_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(4331,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k5_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(3009,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1617,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( m1_pre_topc @ ( k3_pre_topc @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pre_topc) ).
thf(10517,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( m1_pre_topc @ ( k3_pre_topc @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(1348,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(9097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1636,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( v3_tops_1 @ B @ A )
<=> ( v1_tops_3 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_3) ).
thf(10617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( v1_tops_3 @ C @ A ) )
& ( ( v1_tops_3 @ C @ A )
=> ( v3_tops_1 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(4426,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_partfun1) ).
thf(4207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1793,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
<=> ( v3_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tsep_1) ).
thf(11316,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( v3_pre_topc @ C @ A ) )
& ( ( v3_pre_topc @ C @ A )
=> ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(4405,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(857,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc37_tex_2) ).
thf(6320,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(4690,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(5528,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1367,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pre_topc) ).
thf(9227,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(920,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tex_2) ).
thf(6672,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(7578,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1641,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_pre_topc @ ( k3_t_0topsp @ A ) )
& ( l1_pre_topc @ ( k3_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_t_0topsp) ).
thf(10632,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v2_pre_topc @ ( k3_t_0topsp @ A ) )
& ( l1_pre_topc @ ( k3_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(2013,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
& ( m1_connsp_2 @ D @ A @ B ) )
<=> ( m1_connsp_2 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_connsp_2) ).
thf(12288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( m1_connsp_2 @ C @ A @ B )
& ( m1_connsp_2 @ D @ A @ B ) )
=> ( m1_connsp_2 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ A @ B ) )
& ( ( m1_connsp_2 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ A @ B )
=> ( ( m1_connsp_2 @ C @ A @ B )
& ( m1_connsp_2 @ D @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).
thf(1732,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v2_tex_2 @ ( k1_tex_2 @ A @ B ) @ A )
<=> ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tex_2) ).
thf(11062,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( v2_tex_2 @ ( k1_tex_2 @ A @ B ) @ A )
=> ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ( ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v2_tex_2 @ ( k1_tex_2 @ A @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(4868,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(7650,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(6185,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(2994,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(2318,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
<=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(3395,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) )
& ( ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) )
=> ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1971,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_tex_2) ).
thf(12118,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971]) ).
thf(1345,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( m1_pre_topc @ B @ A )
<=> ( ( r1_tarski @ ( k2_pre_topc @ B ) @ ( k2_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ C @ ( u1_pre_topc @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_pre_topc) ).
thf(9069,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( m1_pre_topc @ B @ A )
=> ( ( r1_tarski @ ( k2_pre_topc @ B ) @ ( k2_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ C @ ( u1_pre_topc @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) )
=> ( r2_hidden @ C @ ( u1_pre_topc @ B ) ) ) ) ) ) )
& ( ( ( r1_tarski @ ( k2_pre_topc @ B ) @ ( k2_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ C @ ( u1_pre_topc @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) )
=> ( r2_hidden @ C @ ( u1_pre_topc @ B ) ) ) ) ) )
=> ( m1_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(1585,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( v1_tops_3 @ C @ A )
& ( v1_tops_3 @ E @ B ) )
<=> ( v1_tops_3 @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tops_3) ).
thf(10354,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( ( v1_tops_3 @ C @ A )
& ( v1_tops_3 @ E @ B ) )
=> ( v1_tops_3 @ D @ A ) )
& ( ( v1_tops_3 @ D @ A )
=> ( ( v1_tops_3 @ C @ A )
& ( v1_tops_3 @ E @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(1408,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_tex_2) ).
thf(9430,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(1718,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tops_3) ).
thf(11012,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(1026,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc27_tex_2) ).
thf(7298,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) )
=> ! [C: $i,D: $i] :
( ( ( g1_metric_1 @ A @ B )
= ( g1_metric_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_metric_1) ).
thf(2652,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) )
=> ! [C: $i,D: $i] :
( ( ( g1_metric_1 @ A @ B )
= ( g1_metric_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(254,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(3293,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1330,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v1_connsp_2 @ A )
& ( v5_compts_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C )
& ( v2_connsp_1 @ B @ A )
& ( v2_connsp_1 @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v2_connsp_1 @ D @ A )
& ( v2_connsp_1 @ E @ A )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_connsp_2) ).
thf(8979,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v1_connsp_2 @ A )
& ( v5_compts_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C )
& ( v2_connsp_1 @ B @ A )
& ( v2_connsp_1 @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v2_connsp_1 @ D @ A )
& ( v2_connsp_1 @ E @ A )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funct_2) ).
thf(4735,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(2089,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
<=> ( r1_connsp_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tsep_1) ).
thf(12627,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ C )
=> ( r1_connsp_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) )
& ( ( r1_connsp_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089]) ).
thf(1064,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tsp_1) ).
thf(7539,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(937,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_borsuk_1) ).
thf(6751,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1126,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_tarski @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tex_2) ).
thf(7897,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_tarski @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(576,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_xboole_0 @ ( k1_pre_topc @ A ) )
& ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A )
& ( v1_membered @ ( k1_pre_topc @ A ) )
& ( v2_membered @ ( k1_pre_topc @ A ) )
& ( v3_membered @ ( k1_pre_topc @ A ) )
& ( v4_membered @ ( k1_pre_topc @ A ) )
& ( v5_membered @ ( k1_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_tops_1) ).
thf(4879,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_xboole_0 @ ( k1_pre_topc @ A ) )
& ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A )
& ( v1_membered @ ( k1_pre_topc @ A ) )
& ( v2_membered @ ( k1_pre_topc @ A ) )
& ( v3_membered @ ( k1_pre_topc @ A ) )
& ( v4_membered @ ( k1_pre_topc @ A ) )
& ( v5_membered @ ( k1_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(2002,axiom,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f2_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f3_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(12239,plain,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f2_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f2_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f3_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f3_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(3975,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
=> ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(9639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(1478,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc15_tex_2) ).
thf(9858,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
thf(4566,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(9,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(2202,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(890,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_tdlat_3 @ B )
=> ~ ( v1_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc21_tex_2) ).
thf(6517,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_tdlat_3 @ B )
=> ~ ( v1_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(2015,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(12294,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(1169,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B )
& ~ ( v2_t_0topsp @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_tsp_1) ).
thf(8106,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B )
& ~ ( v2_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(7102,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1843,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_pre_topc @ ( k6_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_tex_4) ).
thf(11579,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_pre_topc @ ( k6_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(2846,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_partfun1) ).
thf(2564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(248,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_membered @ B ) )
=> ( v3_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_membered) ).
thf(3278,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_membered @ B ) )
=> ( v3_membered @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(985,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_3 @ B @ A )
<=> ? [C: $i] :
( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_tex_3) ).
thf(7013,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_3 @ B @ A )
=> ? [C: $i] :
( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ C @ B ) ) )
& ( ? [C: $i] :
( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( m1_pre_topc @ C @ B ) )
=> ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1875,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k1_tarski @ B ) )
=> ( ( k3_pcomps_1 @ A @ C )
= ( k1_tarski @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pcomps_1) ).
thf(11706,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k1_tarski @ B ) )
=> ( ( k3_pcomps_1 @ A @ C )
= ( k1_tarski @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875]) ).
thf(2110,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( k13_borsuk_1 @ A @ B )
= ( k2_funct_3 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) @ ( k10_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_borsuk_1) ).
thf(12701,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( k13_borsuk_1 @ A @ B )
= ( k2_funct_3 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) @ ( k10_funct_3 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110]) ).
thf(1677,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tex_2) ).
thf(10788,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
=> ( v1_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(1809,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_subset_1) ).
thf(11391,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(6115,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(918,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_tex_2) ).
thf(6664,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1679,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v3_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tex_2) ).
thf(10797,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v3_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(1049,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc32_tex_3) ).
thf(7475,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
thf(3913,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(1986,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_2) ).
thf(12174,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tops_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v2_tops_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986]) ).
thf(105,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) )
& ( v4_membered @ ( k1_tarski @ A ) )
& ( v5_membered @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_membered) ).
thf(2588,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) )
& ( v4_membered @ ( k1_tarski @ A ) )
& ( v5_membered @ ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(7554,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1749,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_compts_1 @ ( k6_borsuk_1 @ A @ B ) @ C @ ( k7_borsuk_1 @ A @ B @ D @ E ) )
=> ( ( ( E != k1_xboole_0 )
=> ( r1_compts_1 @ A @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ C ) @ D ) )
& ( ( D != k1_xboole_0 )
=> ( r1_compts_1 @ B @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ B ) @ ( k13_borsuk_1 @ A @ B ) @ C ) @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_borsuk_1) ).
thf(11126,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_compts_1 @ ( k6_borsuk_1 @ A @ B ) @ C @ ( k7_borsuk_1 @ A @ B @ D @ E ) )
=> ( ( ( E != k1_xboole_0 )
=> ( r1_compts_1 @ A @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ C ) @ D ) )
& ( ( D != k1_xboole_0 )
=> ( r1_compts_1 @ B @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ B ) @ ( k13_borsuk_1 @ A @ B ) @ C ) @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( m1_eqrel_1 @ ( k8_eqrel_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_eqrel_1) ).
thf(4593,plain,
! [A: $i,B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( m1_eqrel_1 @ ( k8_eqrel_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1649,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_tex_2 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v5_tex_2 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tex_2) ).
thf(10653,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_tex_2 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v5_tex_2 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(1778,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(11230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2942,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(439,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_partfun1) ).
thf(4255,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(1881,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v4_pre_topc @ ( k1_connsp_2 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_connsp_2) ).
thf(11738,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v4_pre_topc @ ( k1_connsp_2 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881]) ).
thf(742,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_struct_0 @ A )
<=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(5716,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_struct_0 @ A )
=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_xboole_0 @ ( u1_struct_0 @ A ) )
=> ( v3_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(8592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(2172,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r2_tsep_1 @ A @ C @ B ) )
=> ( r2_tsep_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tsep_1) ).
thf(12918,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r2_tsep_1 @ A @ C @ B ) )
=> ( r2_tsep_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2172]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(7087,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(2106,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v3_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_tex_3) ).
thf(12684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v3_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106]) ).
thf(1148,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ~ ( r1_xboole_0 @ B @ C )
& ~ ( r1_tarski @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tex_4) ).
thf(8003,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ~ ( r1_xboole_0 @ B @ C )
& ~ ( r1_tarski @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ~ ( r1_xboole_0 @ B @ C )
& ~ ( r1_tarski @ B @ C ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(126,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_tops_2 @ C @ A @ B )
<=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ( v5_pre_topc @ C @ A @ B )
& ( v5_pre_topc @ ( k2_tops_2 @ A @ B @ C ) @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tops_2) ).
thf(2715,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_tops_2 @ C @ A @ B )
=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ( v5_pre_topc @ C @ A @ B )
& ( v5_pre_topc @ ( k2_tops_2 @ A @ B @ C ) @ B @ A ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C )
& ( v5_pre_topc @ C @ A @ B )
& ( v5_pre_topc @ ( k2_tops_2 @ A @ B @ C ) @ B @ A ) )
=> ( v3_tops_2 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1136,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_tex_4) ).
thf(7942,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(881,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc28_tex_2) ).
thf(6472,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1930,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_tex_4) ).
thf(11909,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).
thf(298,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_relat_2 @ ( k1_t_0topsp @ A ) )
& ( v8_relat_2 @ ( k1_t_0topsp @ A ) )
& ( v1_partfun1 @ ( k1_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k1_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_t_0topsp) ).
thf(3507,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_relat_2 @ ( k1_t_0topsp @ A ) )
& ( v8_relat_2 @ ( k1_t_0topsp @ A ) )
& ( v1_partfun1 @ ( k1_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k1_t_0topsp @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
& ( r3_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_binop_1) ).
thf(5294,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
& ( r3_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1624,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( r1_connsp_1 @ A @ B @ C ) )
=> ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_tsep_1) ).
thf(10540,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( r1_connsp_1 @ A @ B @ C ) )
=> ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_2) ).
thf(3842,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1915,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(11857,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(5125,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1014,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ~ ( v4_tex_3 @ B @ A ) )
=> ( v3_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tex_3) ).
thf(7211,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ~ ( v4_tex_3 @ B @ A ) )
=> ( v3_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(585,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(4937,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(971,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tsp_1) ).
thf(6934,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1838,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( m1_pre_topc @ B @ C )
=> ( v1_tex_3 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tex_3) ).
thf(11562,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( m1_pre_topc @ B @ C )
=> ( v1_tex_3 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(6885,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(586,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
= ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funcop_1) ).
thf(4939,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
= ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(696,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( r2_hidden @ E @ D )
& ( ( k8_funct_2 @ A @ B @ C @ E )
= ( k8_funct_2 @ A @ B @ C @ F ) ) )
=> ( r2_hidden @ F @ D ) ) ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ D ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_t_0topsp) ).
thf(5478,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( r2_hidden @ E @ D )
& ( ( k8_funct_2 @ A @ B @ C @ E )
= ( k8_funct_2 @ A @ B @ C @ F ) ) )
=> ( r2_hidden @ F @ D ) ) ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ D ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(686,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(5399,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_relat_1) ).
thf(4366,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(3082,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(2021,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ C )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ D ) ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_t_0topsp) ).
thf(12313,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ C )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ D ) ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021]) ).
thf(1901,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( u1_struct_0 @ B ) )
& ( v1_tex_4 @ C @ A ) )
=> ( v2_tdlat_3 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tex_4) ).
thf(11808,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( u1_struct_0 @ B ) )
& ( v1_tex_4 @ C @ A ) )
=> ( v2_tdlat_3 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901]) ).
thf(1693,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_tops_1) ).
thf(10856,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C ) ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(788,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( k6_borsuk_1 @ A @ B ) )
<=> ( ( ( u1_struct_0 @ C )
= ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_pre_topc @ C )
= ( a_3_0_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_borsuk_1) ).
thf(5944,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( C
= ( k6_borsuk_1 @ A @ B ) )
=> ( ( ( u1_struct_0 @ C )
= ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_pre_topc @ C )
= ( a_3_0_borsuk_1 @ A @ B @ C ) ) ) )
& ( ( ( ( u1_struct_0 @ C )
= ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_pre_topc @ C )
= ( a_3_0_borsuk_1 @ A @ B @ C ) ) )
=> ( C
= ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(501,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r1_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_binop_1) ).
thf(4534,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r1_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) )
=> ( r1_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(329,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( ( v3_tex_3 @ B @ A )
| ( v3_tex_3 @ C @ A ) )
& ~ ( r1_tsep_1 @ A @ B @ C )
& ~ ( v3_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tex_3) ).
thf(3659,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( ( v3_tex_3 @ B @ A )
| ( v3_tex_3 @ C @ A ) )
& ~ ( r1_tsep_1 @ A @ B @ C )
& ~ ( v3_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1281,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v1_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc38_tex_2) ).
thf(8701,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v1_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(425,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(4200,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(2153,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_tops_1) ).
thf(12858,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2153]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5980,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1652,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v2_t_0topsp @ A )
<=> ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tsp_1) ).
thf(10667,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ( v2_t_0topsp @ A )
=> ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) )
& ( ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) )
=> ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(1879,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tex_3) ).
thf(11726,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v4_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v3_tops_1 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v3_tops_1 @ C @ A ) ) )
=> ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879]) ).
thf(236,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_partfun1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_partfun1) ).
thf(3228,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_partfun1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1846,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(11594,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(4641,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1914,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(11855,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914]) ).
thf(1165,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ ( k5_pre_topc @ A @ ( k16_borsuk_1 @ A @ B ) @ ( k17_borsuk_1 @ A @ B ) @ ( k1_struct_0 @ ( k16_borsuk_1 @ A @ B ) @ C ) ) )
=> ( m1_connsp_2 @ ( k4_pre_topc @ A @ ( k16_borsuk_1 @ A @ B ) @ ( k17_borsuk_1 @ A @ B ) @ D ) @ ( k16_borsuk_1 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_borsuk_1) ).
thf(8096,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ ( k5_pre_topc @ A @ ( k16_borsuk_1 @ A @ B ) @ ( k17_borsuk_1 @ A @ B ) @ ( k1_struct_0 @ ( k16_borsuk_1 @ A @ B ) @ C ) ) )
=> ( m1_connsp_2 @ ( k4_pre_topc @ A @ ( k16_borsuk_1 @ A @ B ) @ ( k17_borsuk_1 @ A @ B ) @ D ) @ ( k16_borsuk_1 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_partfun1) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(579,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(4894,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1216,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_funct_1 @ ( k12_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k12_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) )
& ( m2_relset_1 @ ( k12_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_borsuk_1) ).
thf(8350,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_funct_1 @ ( k12_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k12_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) )
& ( m2_relset_1 @ ( k12_borsuk_1 @ A @ B ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
<=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(8364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( A = C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(1785,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_tsp_1) ).
thf(11252,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k4_pre_topc @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_pre_topc) ).
thf(2850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k4_pre_topc @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1942,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ C @ B ) )
=> ( v4_tex_3 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tex_3) ).
thf(11988,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v4_tex_3 @ B @ A )
& ( m1_pre_topc @ C @ B ) )
=> ( v4_tex_3 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).
thf(757,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tex_3) ).
thf(5790,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(867,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k2_pre_topc @ A ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k1_pre_topc @ A ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k1_pre_topc @ A ) )
=> ( B
= ( k2_pre_topc @ A ) ) )
& ( ( B
= ( u1_struct_0 @ A ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= k1_xboole_0 ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= k1_xboole_0 )
=> ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tops_3) ).
thf(6384,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k2_pre_topc @ A ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k1_pre_topc @ A ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k1_pre_topc @ A ) )
=> ( B
= ( k2_pre_topc @ A ) ) )
& ( ( B
= ( u1_struct_0 @ A ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= k1_xboole_0 ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= k1_xboole_0 )
=> ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(4314,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1991,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tex_4) ).
thf(12187,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991]) ).
thf(1507,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ( ( v2_t_0topsp @ B )
<=> ( ( v3_struct_0 @ B )
| ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_tsp_1) ).
thf(9991,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ( ( ( v2_t_0topsp @ B )
=> ( ( v3_struct_0 @ B )
| ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ) )
& ( ( ( v3_struct_0 @ B )
| ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) )
=> ( v2_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_partfun1) ).
thf(2688,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(874,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(6421,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(1786,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ C )
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_borsuk_1) ).
thf(11295,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ C )
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(708,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(5555,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(195,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( D
= ( k2_tsep_1 @ A @ B @ C ) )
<=> ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tsep_1) ).
thf(3026,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_pre_topc @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( ( D
= ( k2_tsep_1 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) )
& ( ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( D
= ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ B @ B )
& ( m2_relset_1 @ C @ B @ B ) )
=> ~ ( ( r2_hidden @ A @ ( k7_eqrel_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( A
!= ( k6_eqrel_1 @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_eqrel_1) ).
thf(3127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ B @ B )
& ( m2_relset_1 @ C @ B @ B ) )
=> ~ ( ( r2_hidden @ A @ ( k7_eqrel_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( A
!= ( k6_eqrel_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1867,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v6_compts_1 @ C @ A )
<=> ( v6_compts_1 @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_borsuk_1) ).
thf(11661,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v6_compts_1 @ C @ A )
=> ( v6_compts_1 @ D @ B ) )
& ( ( v6_compts_1 @ D @ B )
=> ( v6_compts_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v8_relat_2 @ E )
& ( v1_partfun1 @ E @ A @ A )
& ( m2_relset_1 @ E @ A @ A ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ E )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_eqrel_1) ).
thf(3080,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v8_relat_2 @ E )
& ( v1_partfun1 @ E @ A @ A )
& ( m2_relset_1 @ E @ A @ A ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ E )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1818,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tex_4) ).
thf(11428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(5955,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1705,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v2_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tops_3) ).
thf(10915,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v2_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(1267,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(8612,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(689,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ ( k9_relat_1 @ ( k3_funct_3 @ C ) @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tops_2) ).
thf(5431,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ ( k9_relat_1 @ ( k3_funct_3 @ C ) @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1243,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_tex_3) ).
thf(8498,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(1023,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
& ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
!= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ F @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tsep_1) ).
thf(7264,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
& ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
!= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v4_pre_topc @ F @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1445,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tsp_1) ).
thf(9634,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(257,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(3305,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(1936,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_setfam_1 @ B @ ( k3_pcomps_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_pcomps_1) ).
thf(11974,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_setfam_1 @ B @ ( k3_pcomps_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936]) ).
thf(2032,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= B ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ B )
= B ) )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
thf(12364,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= B ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ B )
= B ) )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( v1_setfam_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_eqrel_1) ).
thf(3063,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( v1_setfam_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1435,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(9599,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(122,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(2700,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1232,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r1_connsp_2 @ A @ B )
<=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( r2_hidden @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) )
=> ~ ( ( D = B )
& ( r2_hidden @ B @ ( k1_tops_1 @ ( k3_pre_topc @ A @ C ) @ ( k1_connsp_1 @ ( k3_pre_topc @ A @ C ) @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_connsp_2) ).
thf(8428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_connsp_2 @ A @ B )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( r2_hidden @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) )
=> ~ ( ( D = B )
& ( r2_hidden @ B @ ( k1_tops_1 @ ( k3_pre_topc @ A @ C ) @ ( k1_connsp_1 @ ( k3_pre_topc @ A @ C ) @ D ) ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( r2_hidden @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k3_pre_topc @ A @ C ) ) )
=> ~ ( ( D = B )
& ( r2_hidden @ B @ ( k1_tops_1 @ ( k3_pre_topc @ A @ C ) @ ( k1_connsp_1 @ ( k3_pre_topc @ A @ C ) @ D ) ) ) ) ) ) )
=> ( r1_connsp_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1000,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_borsuk_1) ).
thf(7105,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(3554,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(2071,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(12514,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071]) ).
thf(1656,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ B ) @ ( k7_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_tex_4) ).
thf(10717,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ B ) @ ( k7_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(1090,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( r4_tsep_1 @ A @ B @ C )
<=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ E @ ( k1_tsep_1 @ A @ B @ C ) ) @ C )
& ~ ( ~ ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_tsep_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ F @ ( k1_tsep_1 @ A @ B @ C ) ) @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_tsep_1) ).
thf(7667,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( ( r4_tsep_1 @ A @ B @ C )
=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ E @ ( k1_tsep_1 @ A @ B @ C ) ) @ C )
& ~ ( ~ ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_tsep_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ F @ ( k1_tsep_1 @ A @ B @ C ) ) @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) )
& ( ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ ( k2_tsep_1 @ A @ D @ ( k1_tsep_1 @ A @ B @ C ) ) @ B )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ E @ ( k1_tsep_1 @ A @ B @ C ) ) @ C )
& ~ ( ~ ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_tsep_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ F @ ( k1_tsep_1 @ A @ B @ C ) ) @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(1194,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_tex_3) ).
thf(8216,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(1088,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k4_pcomps_1 @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k4_pcomps_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_pcomps_1) ).
thf(7662,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( k4_pcomps_1 @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k4_pcomps_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(2044,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ C )
& ( r1_xboole_0 @ E @ B )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tsep_1) ).
thf(12419,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ C )
& ( r1_xboole_0 @ E @ B )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ D @ C )
& ( r1_xboole_0 @ E @ B )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A ) ) )
=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044]) ).
thf(1472,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( m1_pre_topc @ B @ C )
& ( m1_pre_topc @ C @ B ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tsep_1) ).
thf(9809,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( m1_pre_topc @ B @ C )
& ( m1_pre_topc @ C @ B ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(1137,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_tex_3) ).
thf(7947,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A )
& ( v4_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_relat_1) ).
thf(3823,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1320,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_3) ).
thf(8917,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(5560,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(2337,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(6125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(628,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
thf(5154,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(358,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_partfun1) ).
thf(3828,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1225,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tex_3) ).
thf(8391,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_tsep_1 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1306,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tops_2) ).
thf(8840,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(1763,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v3_tex_3 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tex_3) ).
thf(11180,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v3_tex_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v2_tops_1 @ C @ A ) ) )
=> ( v3_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(1404,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(9413,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(2903,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1863,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_1_borsuk_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k12_mcart_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ B ) )
& ( r2_hidden @ E @ ( u1_pre_topc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_borsuk_1) ).
thf(11637,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_borsuk_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k12_mcart_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ B ) )
& ( r2_hidden @ E @ ( u1_pre_topc @ C ) ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k12_mcart_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ B ) )
& ( r2_hidden @ E @ ( u1_pre_topc @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_1_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863]) ).
thf(266,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_partfun1) ).
thf(3359,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1004,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v2_pre_topc @ A )
<=> ( ( r2_hidden @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( u1_pre_topc @ A ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
& ( r2_hidden @ C @ ( u1_pre_topc @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_pre_topc) ).
thf(7127,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ( v2_pre_topc @ A )
=> ( ( r2_hidden @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( u1_pre_topc @ A ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
& ( r2_hidden @ C @ ( u1_pre_topc @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) ) )
& ( ( ( r2_hidden @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( u1_pre_topc @ A ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
& ( r2_hidden @ C @ ( u1_pre_topc @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) )
=> ( v2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(9963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(859,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_connsp_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_tsep_1 @ A @ D @ E )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tsep_1) ).
thf(6330,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_tsep_1 @ A @ D @ E )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_tsep_1 @ A @ D @ E )
& ( r1_tarski @ B @ D )
& ( r1_tarski @ C @ E )
& ( r1_xboole_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) )
=> ( r1_connsp_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(3853,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(836,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( m1_pre_topc @ E @ A ) )
=> ( ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ( r4_tsep_1 @ A @ C @ B ) )
=> ( ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ C @ D ) @ ( k1_tsep_1 @ A @ B @ E ) )
& ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ C ) @ ( k1_tsep_1 @ A @ E @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_tsep_1) ).
thf(6206,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( m1_pre_topc @ E @ A ) )
=> ( ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ( r4_tsep_1 @ A @ C @ B ) )
=> ( ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ C @ D ) @ ( k1_tsep_1 @ A @ B @ E ) )
& ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ C ) @ ( k1_tsep_1 @ A @ E @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(1409,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A )
& ( v4_pre_topc @ D @ A )
& ( v2_tops_1 @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) )
= B )
& ( r1_xboole_0 @ C @ D )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tops_3) ).
thf(9435,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A )
& ( v4_pre_topc @ D @ A )
& ( v2_tops_1 @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) )
= B )
& ( r1_xboole_0 @ C @ D )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(1615,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ( ( k6_pre_topc @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_3) ).
thf(10509,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= ( u1_struct_0 @ A ) ) )
& ( ( ( k6_pre_topc @ A @ B )
= ( u1_struct_0 @ A ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(346,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(3769,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(75,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_2 @ A )
<=> ( A
= ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_2) ).
thf(2468,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_2 @ A )
=> ( A
= ( k4_relat_1 @ A ) ) )
& ( ( A
= ( k4_relat_1 @ A ) )
=> ( v3_relat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(2159,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
thf(12871,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B != A ) )
& ( ( B != A )
=> ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159]) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(5277,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(2070,axiom,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(12512,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070]) ).
thf(2090,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ B )
=> ( m1_pre_topc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tsep_1) ).
thf(12630,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ B )
=> ( m1_pre_topc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090]) ).
thf(2004,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
= ( k6_pre_topc @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tops_1) ).
thf(12262,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
= ( k6_pre_topc @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(8061,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(8850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(1078,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_tarski @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_tex_2) ).
thf(7612,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ D )
= ( k1_tarski @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_funct_2) ).
thf(2728,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1598,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tsep_1) ).
thf(10432,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(1162,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( a_2_4_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_4_tex_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tex_4) ).
thf(8087,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( a_2_4_tex_4 @ A @ B )
!= k1_xboole_0 )
=> ( r1_tarski @ ( k2_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_4_tex_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(3366,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1953,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_3_borsuk_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_struct_0 @ B @ D ) )
& ~ ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_borsuk_1) ).
thf(12039,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_borsuk_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_struct_0 @ B @ D ) )
& ~ ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_struct_0 @ B @ D ) )
& ~ ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_3_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( v1_xboole_0 @ B )
=> ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funcop_1) ).
thf(2675,plain,
! [A: $i,B: $i] :
( ( v1_xboole_0 @ B )
=> ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(625,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ~ ( v1_xboole_0 @ ( k8_eqrel_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_borsuk_1) ).
thf(5147,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ~ ( v1_xboole_0 @ ( k8_eqrel_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1532,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(10129,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v3_tsp_1 @ B @ A )
<=> ( v2_t_0topsp @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_v3_tsp_1) ).
thf(7752,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( v3_tsp_1 @ B @ A )
=> ( v2_t_0topsp @ B ) )
& ( ( v2_t_0topsp @ B )
=> ( v3_tsp_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(2026,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_tex_4) ).
thf(12328,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_pre_topc @ ( k7_tex_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026]) ).
thf(82,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v1_relat_2 @ A )
=> ( v1_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_2) ).
thf(2500,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v1_relat_2 @ A )
=> ( v1_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1622,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tops_2 @ B @ A )
& ( v2_tops_2 @ C @ A ) )
=> ( v2_tops_2 @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tops_2) ).
thf(10536,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tops_2 @ B @ A )
& ( v2_tops_2 @ C @ A ) )
=> ( v2_tops_2 @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(2049,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k7_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc19_tex_4) ).
thf(12439,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k7_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049]) ).
thf(592,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(4959,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1057,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_t_0topsp @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k8_borsuk_1 @ A @ A @ D @ E ) @ ( k1_t_0topsp @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_t_0topsp) ).
thf(7515,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_t_0topsp @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k8_borsuk_1 @ A @ A @ D @ E ) @ ( k1_t_0topsp @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1256,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( m1_pre_topc @ E @ A )
& ( r4_tsep_1 @ A @ D @ E )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_tsep_1) ).
thf(8547,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r3_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( m1_pre_topc @ E @ A )
& ( r4_tsep_1 @ A @ D @ E )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) )
& ( ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( m1_pre_topc @ E @ A )
& ( r4_tsep_1 @ A @ D @ E )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) )
=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(1132,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v3_realset2 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_tex_2) ).
thf(7919,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v3_realset2 @ B )
& ( v2_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( m1_subset_1 @ ( k6_eqrel_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_eqrel_1) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ( m1_subset_1 @ ( k6_eqrel_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(4624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) )
=> ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1357,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_tsp_1) ).
thf(9151,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ( r2_hidden @ C @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) )
& ( r1_tarski @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(520,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
= ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funcop_1) ).
thf(4611,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
= ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1908,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v2_tops_1 @ C @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v2_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_tops_1) ).
thf(11830,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v2_tops_1 @ C @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v2_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ D )
=> ( ( r1_tarski @ E @ C )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
& ( E
= ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_borsuk_1) ).
thf(7461,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ D )
=> ( ( r1_tarski @ E @ C )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
& ( E
= ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(487,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(4436,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(92,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
& ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(2543,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
& ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1729,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( v2_connsp_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_connsp_2) ).
thf(11054,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_connsp_2 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( v2_connsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(1923,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ ( k3_tex_4 @ A @ C ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tex_4) ).
thf(11882,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ ( k3_tex_4 @ A @ C ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k3_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923]) ).
thf(1538,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(10160,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_binop_1) ).
thf(2279,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) )
=> ( v3_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(7585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1265,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(8602,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(1008,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tdlat_3 @ B )
=> ( v3_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc22_tex_2) ).
thf(7163,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tdlat_3 @ B )
=> ( v3_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_tsep_1 @ A @ B @ C ) )
& ( v1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tsep_1) ).
thf(5809,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_tsep_1 @ A @ B @ C ) )
& ( v1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) )
& ( m1_pre_topc @ ( k1_tsep_1 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1370,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v6_compts_1 @ D @ B )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ ( k6_borsuk_1 @ B @ A ) @ ( k7_borsuk_1 @ B @ A @ D @ ( k1_struct_0 @ A @ C ) ) )
=> ? [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
& ? [G: $i] :
( ( m1_connsp_2 @ G @ A @ C )
& ( r1_tarski @ ( k10_borsuk_1 @ B @ A @ D @ C @ F @ G ) @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_borsuk_1) ).
thf(9242,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v6_compts_1 @ D @ B )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ ( k6_borsuk_1 @ B @ A ) @ ( k7_borsuk_1 @ B @ A @ D @ ( k1_struct_0 @ A @ C ) ) )
=> ? [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
& ? [G: $i] :
( ( m1_connsp_2 @ G @ A @ C )
& ( r1_tarski @ ( k10_borsuk_1 @ B @ A @ D @ C @ F @ G ) @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(1444,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ B @ C ) )
=> ( m2_connsp_2 @ ( k5_borsuk_1 @ A @ B @ C @ D @ E ) @ A @ ( k5_pre_topc @ A @ B @ D @ ( k1_struct_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_borsuk_1) ).
thf(9632,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ B @ C ) )
=> ( m2_connsp_2 @ ( k5_borsuk_1 @ A @ B @ C @ D @ E ) @ A @ ( k5_pre_topc @ A @ B @ D @ ( k1_struct_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(1716,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
<=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tops_1) ).
thf(11005,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k1_tops_1 @ A @ B ) ) ) )
& ( ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k1_tops_1 @ A @ B ) ) )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(2152,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_t_0topsp) ).
thf(12856,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152]) ).
thf(1157,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(8043,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(145,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funcop_1) ).
thf(2807,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(216,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(3156,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1922,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B )
= ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_t_0topsp) ).
thf(11879,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k3_t_0topsp @ A ) ) @ ( k4_t_0topsp @ A ) @ B )
= ( k6_eqrel_1 @ ( u1_struct_0 @ A ) @ ( k1_t_0topsp @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).
thf(817,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(6105,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(6531,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(2145,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( v3_tops_1 @ B @ A )
<=> ( B
= ( k2_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_tops_1) ).
thf(12829,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( B
= ( k2_tops_1 @ A @ B ) ) )
& ( ( B
= ( k2_tops_1 @ A @ B ) )
=> ( v3_tops_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145]) ).
thf(1603,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v2_pre_topc @ ( k1_tex_2 @ A @ B ) )
=> ( ( v1_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v2_tdlat_3 @ ( k1_tex_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_tex_2) ).
thf(10451,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v2_pre_topc @ ( k1_tex_2 @ A @ B ) )
=> ( ( v1_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v2_tdlat_3 @ ( k1_tex_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(908,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( ( v2_tex_3 @ B @ A )
& ( v1_tex_3 @ C @ A ) )
| ( ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ C @ A ) ) )
=> ( ( v1_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_tex_3) ).
thf(6622,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( ( v2_tex_3 @ B @ A )
& ( v1_tex_3 @ C @ A ) )
| ( ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ C @ A ) ) )
=> ( ( v1_tex_3 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(840,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tex_3) ).
thf(6220,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(473,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funcop_1) ).
thf(4392,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1804,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(11369,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(1655,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) )
& ~ ( v1_tex_2 @ ( k3_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_tex_4) ).
thf(10714,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) )
& ~ ( v1_tex_2 @ ( k3_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_partfun1) ).
thf(4278,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(5917,plain,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_partfun1) ).
thf(2696,plain,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(40,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( r1_tarski @ A @ k5_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_membered) ).
thf(2347,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( r1_tarski @ A @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(560,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( r3_tsep_1 @ A @ C @ D )
=> ( ( r1_tsep_1 @ A @ C @ B )
| ( r1_tsep_1 @ A @ D @ B )
| ( ( r3_tsep_1 @ A @ ( k2_tsep_1 @ A @ C @ B ) @ ( k2_tsep_1 @ A @ D @ B ) )
& ( r3_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ ( k2_tsep_1 @ A @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tsep_1) ).
thf(4780,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( r3_tsep_1 @ A @ C @ D )
=> ( ( r1_tsep_1 @ A @ C @ B )
| ( r1_tsep_1 @ A @ D @ B )
| ( ( r3_tsep_1 @ A @ ( k2_tsep_1 @ A @ C @ B ) @ ( k2_tsep_1 @ A @ D @ B ) )
& ( r3_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ ( k2_tsep_1 @ A @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(664,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_pre_topc @ A )
=> ( A
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(5308,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_pre_topc @ A )
=> ( A
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1181,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(8153,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(2792,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1278,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ ( k5_pre_topc @ A @ B @ C @ ( k1_tops_1 @ B @ D ) ) @ ( k1_tops_1 @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_borsuk_1) ).
thf(8681,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ ( k5_pre_topc @ A @ B @ C @ ( k1_tops_1 @ B @ D ) ) @ ( k1_tops_1 @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1548,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ C @ A )
=> ( v2_tops_2 @ ( k1_tops_2 @ A @ B @ C ) @ ( k3_pre_topc @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tops_2) ).
thf(10214,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_2 @ C @ A )
=> ( v2_tops_2 @ ( k1_tops_2 @ A @ B @ C ) @ ( k3_pre_topc @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(848,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(6284,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(220,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(3168,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(65,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(2435,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(250,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(3284,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(970,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
thf(6928,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ C @ D ) ) )
=> ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1036,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) )
| ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tex_4) ).
thf(7363,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) )
| ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ C ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(7099,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(277,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(3400,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(3139,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1666,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( ( v1_tops_2 @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ( ( v1_tops_2 @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ C ) @ A )
& ( v1_tops_2 @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ B ) @ ( k13_borsuk_1 @ A @ B ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_borsuk_1) ).
thf(10754,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( ( v1_tops_2 @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ( ( v1_tops_2 @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( k12_borsuk_1 @ A @ B ) @ C ) @ A )
& ( v1_tops_2 @ ( k14_borsuk_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( u1_struct_0 @ B ) @ ( k13_borsuk_1 @ A @ B ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(1555,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( v3_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_tops_1) ).
thf(10241,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( v3_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(1400,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( r1_borsuk_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tex_2) ).
thf(9395,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( r1_borsuk_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_partfun1) ).
thf(2458,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tex_3) ).
thf(8946,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(2029,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( v3_pre_topc @ E @ B )
<=> ( v3_pre_topc @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tsep_1) ).
thf(12343,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E ) )
=> ( ( ( v3_pre_topc @ E @ B )
=> ( v3_pre_topc @ D @ A ) )
& ( ( v3_pre_topc @ D @ A )
=> ( v3_pre_topc @ E @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(4424,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( D
= ( k5_partfun1 @ A @ B @ C ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ D )
<=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_partfun1) ).
thf(4138,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( D
= ( k5_partfun1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) )
& ( ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) )
=> ( r2_hidden @ E @ D ) ) ) )
& ( ! [E: $i] :
( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) )
& ( ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) )
=> ( r2_hidden @ E @ D ) ) )
=> ( D
= ( k5_partfun1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(2175,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k4_t_0topsp @ A )
= ( k17_borsuk_1 @ A @ ( k2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_t_0topsp) ).
thf(12933,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k4_t_0topsp @ A )
= ( k17_borsuk_1 @ A @ ( k2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175]) ).
thf(2170,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tops_1) ).
thf(12912,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(2479,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1757,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ~ ( v1_realset1 @ ( k6_pre_topc @ A @ B ) )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tex_4) ).
thf(11150,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ~ ( v1_realset1 @ ( k6_pre_topc @ A @ B ) )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(750,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_tex_2) ).
thf(5749,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(457,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(4325,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1486,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_tex_3) ).
thf(9912,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v1_tex_3 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(513,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(4587,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1586,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).
thf(10364,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(1671,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) )
= ( u1_struct_0 @ A ) )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tops_3) ).
thf(10767,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) )
= ( u1_struct_0 @ A ) )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(1683,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v4_pre_topc @ C @ A )
<=> ( v4_pre_topc @ D @ B ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tops_3) ).
thf(10806,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v4_pre_topc @ C @ A )
=> ( v4_pre_topc @ D @ B ) )
& ( ( v4_pre_topc @ D @ B )
=> ( v4_pre_topc @ C @ A ) ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_relset_1) ).
thf(4770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_1_pcomps_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r1_xboole_0 @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_pcomps_1) ).
thf(10464,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_pcomps_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r1_xboole_0 @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r1_xboole_0 @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_1_pcomps_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(1451,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k3_tarski @ ( k5_subset_1 @ B @ C @ D ) )
= ( k3_xboole_0 @ ( k3_tarski @ C ) @ ( k3_tarski @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_borsuk_1) ).
thf(9665,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k3_tarski @ ( k5_subset_1 @ B @ C @ D ) )
= ( k3_xboole_0 @ ( k3_tarski @ C ) @ ( k3_tarski @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(1111,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ( ( v1_tsep_1 @ B @ A )
| ( v1_tsep_1 @ C @ A ) )
=> ( v2_t_0topsp @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_tsp_1) ).
thf(7764,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_t_0topsp @ C )
& ( m2_tsp_1 @ C @ A ) )
=> ( ( ( v1_tsep_1 @ B @ A )
| ( v1_tsep_1 @ C @ A ) )
=> ( v2_t_0topsp @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1938,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(11978,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938]) ).
thf(1619,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ( v1_tsp_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tsp_1) ).
thf(10526,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ( v1_tsp_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(977,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k6_tex_4 @ A @ B ) )
& ~ ( v3_realset2 @ ( k6_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_tex_4) ).
thf(6970,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k6_tex_4 @ A @ B ) )
& ~ ( v3_realset2 @ ( k6_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(3171,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(2960,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(809,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc50_tex_2) ).
thf(6068,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_tdlat_3 @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(4944,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1684,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ ( k2_tex_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tex_4) ).
thf(10821,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_tex_4 @ B @ A )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ ( k2_tex_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(2162,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(12883,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
<=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(6861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(4656,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1821,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m2_connsp_2 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_connsp_2) ).
thf(11450,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m2_connsp_2 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821]) ).
thf(1116,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( v2_tex_3 @ B @ A ) )
=> ( v3_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tex_3) ).
thf(7816,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( v2_tex_3 @ B @ A ) )
=> ( v3_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1546,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v4_pre_topc @ D @ B )
<=> ( v4_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tsep_1) ).
thf(10199,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v4_pre_topc @ D @ B )
=> ( v4_pre_topc @ C @ A ) )
& ( ( v4_pre_topc @ C @ A )
=> ( v4_pre_topc @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(1870,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k1_connsp_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_connsp_2) ).
thf(11681,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k1_connsp_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870]) ).
thf(2061,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tops_2 @ B @ A )
& ( v1_finset_1 @ B ) )
=> ( v4_pre_topc @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_tops_2) ).
thf(12484,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v2_tops_2 @ B @ A )
& ( v1_finset_1 @ B ) )
=> ( v4_pre_topc @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061]) ).
thf(2065,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_0_tex_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_tex_4) ).
thf(12495,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_tex_4 @ A @ B ) @ ( k1_setfam_1 @ ( a_2_0_tex_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).
thf(12,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( v5_membered @ B )
=> ( ( r1_xboole_0 @ A @ B )
<=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_membered) ).
thf(2209,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( v5_membered @ B )
=> ( ( ( r1_xboole_0 @ A @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
=> ( r1_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_eqrel_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_eqrel_1) ).
thf(2743,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v3_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_eqrel_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1833,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tops_3) ).
thf(11541,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833]) ).
thf(1702,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_borsuk_1) ).
thf(10905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(2117,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_connsp_1 @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r4_connsp_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_connsp_2) ).
thf(12722,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_connsp_1 @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r4_connsp_1 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_funct_2) ).
thf(2226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(770,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_tsep_1) ).
thf(5860,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(682,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tops_1) ).
thf(5389,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k21_borsuk_1 @ A @ B @ C )
= ( k16_borsuk_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k21_borsuk_1) ).
thf(8098,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k21_borsuk_1 @ A @ B @ C )
= ( k16_borsuk_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1261,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k3_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k3_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k3_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k3_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tsp_2) ).
thf(8579,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v1_funct_1 @ ( k3_tsp_2 @ A @ B ) )
& ( v1_funct_2 @ ( k3_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ ( k3_tsp_2 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k3_tsp_2 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(6814,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( v1_partfun1 @ D @ A @ B )
& ( r1_partfun1 @ C @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_partfun1) ).
thf(3665,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( v1_partfun1 @ D @ A @ B )
& ( r1_partfun1 @ C @ D ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(6711,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(2054,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ B @ D ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tops_3) ).
thf(12452,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k1_tops_1 @ A @ C )
= ( k1_tops_1 @ B @ D ) ) ) ) ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054]) ).
thf(2019,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_4_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_4_tex_4) ).
thf(12302,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_4_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v4_pre_topc @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_4_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019]) ).
thf(1737,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) )
= ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tops_1) ).
thf(11076,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) )
= ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_binop_1) ).
thf(2594,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(912,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pre_topc) ).
thf(6639,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1262,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).
thf(8584,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ C @ D ) )
<=> ( ( k6_eqrel_1 @ A @ C @ D )
= ( k6_eqrel_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_eqrel_1) ).
thf(3336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ C @ D ) )
=> ( ( k6_eqrel_1 @ A @ C @ D )
= ( k6_eqrel_1 @ A @ C @ B ) ) )
& ( ( ( k6_eqrel_1 @ A @ C @ D )
= ( k6_eqrel_1 @ A @ C @ B ) )
=> ( r2_hidden @ B @ ( k6_eqrel_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1820,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_connsp_2 @ A @ B @ C )
<=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( B = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k3_pre_topc @ A @ D ) ) )
=> ~ ( ( E = C )
& ( r1_connsp_2 @ ( k3_pre_topc @ A @ D ) @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_connsp_2) ).
thf(11433,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_connsp_2 @ A @ B @ C )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( B = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k3_pre_topc @ A @ D ) ) )
=> ~ ( ( E = C )
& ( r1_connsp_2 @ ( k3_pre_topc @ A @ D ) @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( B = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k3_pre_topc @ A @ D ) ) )
=> ~ ( ( E = C )
& ( r1_connsp_2 @ ( k3_pre_topc @ A @ D ) @ E ) ) ) ) )
=> ( r2_connsp_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).
thf(1095,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k2_pre_topc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_2) ).
thf(7700,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_pre_topc @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k2_pre_topc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(564,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k12_mcart_1 @ A @ C @ E @ F ) )
= ( k12_mcart_1 @ B @ C @ ( k2_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_borsuk_1) ).
thf(4834,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k12_mcart_1 @ A @ C @ E @ F ) )
= ( k12_mcart_1 @ B @ C @ ( k2_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1517,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_t_0topsp @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_t_0topsp @ B ) ) )
& ( A = C )
& ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_t_0topsp) ).
thf(10077,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_t_0topsp @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_t_0topsp @ B ) ) )
& ( A = C )
& ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ B ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_t_0topsp @ B ) ) )
& ( A = C )
& ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ B ) ) )
=> ( r2_hidden @ A @ ( a_1_0_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(290,axiom,
! [A: $i] :
( ( v3_relat_2 @ ( k6_partfun1 @ A ) )
& ( v8_relat_2 @ ( k6_partfun1 @ A ) )
& ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_eqrel_1) ).
thf(3465,plain,
! [A: $i] :
( ( v3_relat_2 @ ( k6_partfun1 @ A ) )
& ( v8_relat_2 @ ( k6_partfun1 @ A ) )
& ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(604,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(5055,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(965,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(6903,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1515,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v3_compts_1 @ A )
=> ( v4_pre_topc @ ( k1_struct_0 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_pcomps_1) ).
thf(10072,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v3_compts_1 @ A )
=> ( v4_pre_topc @ ( k1_struct_0 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(745,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v5_tex_2 @ B @ A )
<=> ( ( v1_tdlat_3 @ B )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tdlat_3 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tex_2) ).
thf(5724,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( v5_tex_2 @ B @ A )
=> ( ( v1_tdlat_3 @ B )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tdlat_3 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) ) )
& ( ( ( v1_tdlat_3 @ B )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tdlat_3 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) )
= ( g1_pre_topc @ ( u1_struct_0 @ C ) @ ( u1_pre_topc @ C ) ) ) ) ) )
=> ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( ( v1_membered @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc42_membered) ).
thf(6818,plain,
! [A: $i,B: $i] :
( ( ( v1_membered @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1086,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funcop_1) ).
thf(7653,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(348,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( v1_funct_1 @ ( u1_metric_1 @ A ) )
& ( v1_funct_2 @ ( u1_metric_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( m2_relset_1 @ ( u1_metric_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_metric_1) ).
thf(3789,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( v1_funct_1 @ ( u1_metric_1 @ A ) )
& ( v1_funct_2 @ ( u1_metric_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers )
& ( m2_relset_1 @ ( u1_metric_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ k1_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ D @ E )
!= ( k1_funct_1 @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_funct_2) ).
thf(3709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ D @ E )
!= ( k1_funct_1 @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(3825,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1035,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v5_pre_topc @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) @ ( k5_pre_topc @ A @ B @ C @ ( k6_pre_topc @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tops_2) ).
thf(7359,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) @ ( k5_pre_topc @ A @ B @ C @ ( k6_pre_topc @ B @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_pre_topc @ A @ B @ C @ D ) ) @ ( k5_pre_topc @ A @ B @ C @ ( k6_pre_topc @ B @ D ) ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(2132,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( m1_pre_topc @ B @ C )
=> ( v2_tex_3 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tex_3) ).
thf(12775,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( m1_pre_topc @ B @ C )
=> ( v2_tex_3 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132]) ).
thf(536,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [D: $i] :
( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( ( k1_relat_1 @ D )
= C )
& ( ( k2_relat_1 @ D )
= ( k1_tops_2 @ A @ B @ C ) )
& ! [E: $i] :
( ( r2_hidden @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( F = E )
=> ( ( k1_funct_1 @ D @ E )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tops_2) ).
thf(4666,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [D: $i] :
( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( ( k1_relat_1 @ D )
= C )
& ( ( k2_relat_1 @ D )
= ( k1_tops_2 @ A @ B @ C ) )
& ! [E: $i] :
( ( r2_hidden @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( F = E )
=> ( ( k1_funct_1 @ D @ E )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1909,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A )
& ( v3_tops_1 @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= B )
& ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tops_3) ).
thf(11832,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ C @ A )
& ( v1_tops_1 @ C @ A )
& ( v3_tops_1 @ D @ A )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= B )
& ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).
thf(637,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relset_1) ).
thf(5191,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1723,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tsp_1) ).
thf(11039,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k7_tex_4 @ A @ B ) )
& ~ ( v3_realset2 @ ( k7_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc20_tex_4) ).
thf(5351,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k7_tex_4 @ A @ B ) )
& ~ ( v3_realset2 @ ( k7_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k7_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1146,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_pre_topc) ).
thf(7996,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(2072,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k2_tex_4 @ A @ C ) )
<=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
!= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tex_4) ).
thf(12516,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k2_tex_4 @ A @ C ) )
=> ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
!= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) )
& ( ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
!= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
=> ( r1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k2_tex_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1010,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ ( k1_struct_0 @ A @ B ) ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_tex_4) ).
thf(7167,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( g1_pre_topc @ ( u1_struct_0 @ ( k5_tex_4 @ A @ B ) ) @ ( u1_pre_topc @ ( k5_tex_4 @ A @ B ) ) )
= ( g1_pre_topc @ ( u1_struct_0 @ ( k7_tex_4 @ A @ ( k1_struct_0 @ A @ B ) ) ) @ ( u1_pre_topc @ ( k7_tex_4 @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1309,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tops_1) ).
thf(8854,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1576,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(10325,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(1390,axiom,
! [A: $i] : ( v2_compts_1 @ ( k2_pcomps_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_pcomps_1) ).
thf(9343,plain,
! [A: $i] : ( v2_compts_1 @ ( k2_pcomps_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(1919,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_connsp_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_connsp_2) ).
thf(11867,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_connsp_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(5813,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(941,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(6770,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1597,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E )
& ( v2_tops_1 @ D @ A ) )
=> ( v2_tops_1 @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tops_3) ).
thf(10428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( r1_tarski @ C @ ( u1_struct_0 @ B ) )
& ( r1_tarski @ D @ C )
& ( D = E )
& ( v2_tops_1 @ D @ A ) )
=> ( v2_tops_1 @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(648,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( r4_tsep_1 @ A @ B @ C )
=> ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ D ) @ ( k1_tsep_1 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_tsep_1) ).
thf(5228,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ( r4_tsep_1 @ A @ B @ C )
=> ( r4_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ D ) @ ( k1_tsep_1 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1285,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relset_1) ).
thf(8722,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(885,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(6494,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(187,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(3003,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k18_borsuk_1 @ A @ B @ C ) )
& ( m1_eqrel_1 @ ( k18_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_borsuk_1) ).
thf(5394,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k18_borsuk_1 @ A @ B @ C ) )
& ( m1_eqrel_1 @ ( k18_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(258,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(3331,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1968,axiom,
m1_subset_1 @ k24_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k24_borsuk_1) ).
thf(12113,plain,
m1_subset_1 @ k24_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(5104,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(3368,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(2039,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(12387,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039]) ).
thf(1955,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_tops_1) ).
thf(12050,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(3662,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(58,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_relat_1) ).
thf(2416,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1741,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_struct_0) ).
thf(11091,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(1755,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( k2_tsp_2 @ A @ B )
= ( k1_tsp_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_tsp_2) ).
thf(11145,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( k2_tsp_2 @ A @ B )
= ( k1_tsp_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k5_relset_1 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(4261,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k5_relset_1 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(1931,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( k1_connsp_2 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ E @ D )
<=> ( ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ E @ A )
& ( r2_hidden @ B @ E ) ) ) )
& ( ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ D )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_connsp_2) ).
thf(11918,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( k1_connsp_2 @ A @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ E @ D )
=> ( ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ E @ A )
& ( r2_hidden @ B @ E ) ) )
& ( ( ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ E @ A )
& ( r2_hidden @ B @ E ) )
=> ( r2_hidden @ E @ D ) ) ) )
& ( ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ D )
= C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ E @ D )
=> ( ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ E @ A )
& ( r2_hidden @ B @ E ) ) )
& ( ( ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ E @ A )
& ( r2_hidden @ B @ E ) )
=> ( r2_hidden @ E @ D ) ) ) )
& ( ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ D )
= C ) )
=> ( C
= ( k1_connsp_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931]) ).
thf(1033,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( ( B != k1_xboole_0 )
& ( ( k7_setfam_1 @ A @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k7_setfam_1 @ A @ B )
!= k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
thf(7327,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( ( B != k1_xboole_0 )
& ( ( k7_setfam_1 @ A @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k7_setfam_1 @ A @ B )
!= k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_relat_1) ).
thf(4182,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(4293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(658,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_borsuk_1 @ B @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_setfam_1 @ B )
& ( v2_borsuk_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_borsuk_1) ).
thf(5287,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_borsuk_1 @ B @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_setfam_1 @ B )
& ( v2_borsuk_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1710,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v4_tex_3 @ B @ A )
<=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tex_3) ).
thf(10937,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v4_tex_3 @ B @ A )
=> ( v3_tops_1 @ C @ A ) )
& ( ( v3_tops_1 @ C @ A )
=> ( v4_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(8172,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1824,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ~ ( v1_xboole_0 @ B )
<=> ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tex_3) ).
thf(11497,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( ~ ( v1_xboole_0 @ B )
=> ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ( ( v1_tex_2 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824]) ).
thf(1477,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) )
=> ( r2_hidden @ D @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_borsuk_1) ).
thf(9856,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) )
=> ( r2_hidden @ D @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(224,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( k4_pre_topc @ A @ B @ C @ D )
= ( k5_pre_topc @ B @ A @ ( k2_tops_2 @ A @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tops_2) ).
thf(3181,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( k4_pre_topc @ A @ B @ C @ D )
= ( k5_pre_topc @ B @ A @ ( k2_tops_2 @ A @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(52,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(2384,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) )
& ( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1241,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v5_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc42_tex_2) ).
thf(8488,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v5_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_tarski @ D @ C ) )
=> ( r1_partfun1 @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_partfun1) ).
thf(2786,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_tarski @ D @ C ) )
=> ( r1_partfun1 @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1988,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_4 @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_tex_4) ).
thf(12181,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_4 @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k1_tex_4 @ A @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988]) ).
thf(1414,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k2_pcomps_1 @ A ) )
& ( v1_pre_topc @ ( k2_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k2_pcomps_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pcomps_1) ).
thf(9470,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k2_pcomps_1 @ A ) )
& ( v1_pre_topc @ ( k2_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k2_pcomps_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E )
& ( v1_partfun1 @ E @ A @ B ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_partfun1) ).
thf(4321,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E )
& ( v1_partfun1 @ E @ A @ B ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_partfun1) ).
thf(2399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(884,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( C = D )
| ( r1_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tex_2) ).
thf(6484,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( C = D )
| ( r1_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( C = D )
| ( r1_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ D ) ) ) ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(2007,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( v1_tops_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tops_1) ).
thf(12273,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( v1_tops_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007]) ).
thf(1305,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_tex_2) ).
thf(8837,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(1244,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relset_1) ).
thf(8501,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
=> ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(820,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_tex_3 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_tex_3) ).
thf(6118,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_tex_3 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ B )
=> ( ( ( r2_hidden @ C @ B )
& ( A != C ) )
| ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(7715,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ B )
=> ( ( ( r2_hidden @ C @ B )
& ( A != C ) )
| ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(2024,axiom,
? [A: $i] : ( l1_pre_topc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(12323,plain,
? [A: $i] : ( l1_pre_topc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024]) ).
thf(1273,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v5_pre_topc @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k4_borsuk_1 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_borsuk_1) ).
thf(8638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v5_pre_topc @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k4_borsuk_1 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(245,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(3267,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ C )
= ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_partfun1) ).
thf(4774,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ C )
= ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1209,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k6_pre_topc @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tops_1) ).
thf(8304,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k6_pre_topc @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(1866,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
<=> ( v1_tops_1 @ ( k1_tops_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tops_3) ).
thf(11658,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
=> ( v1_tops_1 @ ( k1_tops_1 @ A @ B ) @ A ) )
& ( ( v1_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
=> ( v1_tops_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).
thf(1903,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v3_tex_2 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tex_2) ).
thf(11815,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v3_tex_2 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).
thf(1835,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tex_4) ).
thf(11552,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835]) ).
thf(1803,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) )
& ~ ( v1_realset1 @ ( k3_tex_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_tex_4) ).
thf(11366,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_tex_4 @ A @ B ) )
& ~ ( v1_realset1 @ ( k3_tex_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
<=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
thf(4387,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) )
& ( ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1811,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( k3_tex_4 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tex_4) ).
thf(11405,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( k3_tex_4 @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(871,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( k4_pcomps_1 @ A ) )
& ( r2_hidden @ C @ ( k4_pcomps_1 @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k4_pcomps_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_pcomps_1) ).
thf(6412,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( k4_pcomps_1 @ A ) )
& ( r2_hidden @ C @ ( k4_pcomps_1 @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k4_pcomps_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1823,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_tsp_1) ).
thf(11454,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ C @ E )
& ~ ( r2_hidden @ D @ E ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ~ ( r2_hidden @ C @ E )
& ( r2_hidden @ D @ E ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v2_membered @ B ) )
=> ( v2_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_membered) ).
thf(3529,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v2_membered @ B ) )
=> ( v2_membered @ ( k1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(334,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(3677,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1007,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( ( v3_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tex_2) ).
thf(7157,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( ( v3_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A )
& ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A )
& ( v3_tex_2 @ B @ A )
& ( v3_tex_2 @ C @ A ) )
=> ( v3_tex_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(1496,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tex_2) ).
thf(9955,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(1777,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k2_tops_1 @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tops_1) ).
thf(11227,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k2_tops_1 @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(2053,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v3_realset2 @ ( k1_tex_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tex_2) ).
thf(12448,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v3_realset2 @ ( k1_tex_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( v5_membered @ A )
& ( v5_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc46_membered) ).
thf(3793,plain,
! [A: $i,B: $i] :
( ( ( v5_membered @ A )
& ( v5_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(2103,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tex_4) ).
thf(12675,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_tex_4 @ A @ B )
= ( k3_tex_4 @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r4_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_binop_1) ).
thf(2680,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r4_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( m1_connsp_2 @ ( k9_borsuk_1 @ A @ B @ C @ D @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k8_borsuk_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_borsuk_1) ).
thf(12152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( m1_connsp_2 @ ( k9_borsuk_1 @ A @ B @ C @ D @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k8_borsuk_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979]) ).
thf(1519,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tops_1) ).
thf(10087,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(5144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1470,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(9799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1326,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_membered @ B ) )
=> ( v1_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_membered) ).
thf(8953,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_membered @ B ) )
=> ( v1_membered @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(1450,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( k7_borsuk_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) @ ( k12_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= C )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) @ ( k13_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_borsuk_1) ).
thf(9660,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( k7_borsuk_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ A ) ) @ ( k12_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= C )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) @ ( k1_pcomps_1 @ ( u1_struct_0 @ B ) ) @ ( k13_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(1059,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v3_tdlat_3 @ A ) )
=> ( v3_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_tex_2) ).
thf(7520,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v3_tdlat_3 @ A ) )
=> ( v3_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(7574,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(5672,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1893,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v2_tops_2 @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) ) )
=> ( ( D = B )
=> ( v2_tops_2 @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tops_2) ).
thf(11772,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( v2_tops_2 @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) ) )
=> ( ( D = B )
=> ( v2_tops_2 @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(5128,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( r2_tarski @ A @ B )
<=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( D = F )
<=> ( E = G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tarski) ).
thf(4098,plain,
! [A: $i,B: $i] :
( ( ( r2_tarski @ A @ B )
=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) ) )
& ( ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) )
=> ( r2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v1_funct_2 @ C @ A @ B )
<=> ( A
= ( k4_relset_1 @ A @ B @ C ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( ( v1_funct_2 @ C @ A @ B )
<=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(4570,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v1_funct_2 @ C @ A @ B )
=> ( A
= ( k4_relset_1 @ A @ B @ C ) ) )
& ( ( A
= ( k4_relset_1 @ A @ B @ C ) )
=> ( v1_funct_2 @ C @ A @ B ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( ( ( v1_funct_2 @ C @ A @ B )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1925,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k2_tex_4 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_tex_4) ).
thf(11894,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k2_tex_4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(5196,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(4372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1358,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(9162,plain,
! [A: $i,B: $i] :
( ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( ( v4_membered @ A )
& ( v4_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc45_membered) ).
thf(3761,plain,
! [A: $i,B: $i] :
( ( ( v4_membered @ A )
& ( v4_membered @ B ) )
=> ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k5_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1447,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r3_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_tsep_1) ).
thf(9643,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r3_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) ) )
& ( ? [D: $i] :
( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A )
& ? [E: $i] :
( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A )
& ( m1_pre_topc @ B @ D )
& ( m1_pre_topc @ C @ E )
& ( ( r1_tsep_1 @ A @ D @ E )
| ( r1_tsep_1 @ A @ ( k2_tsep_1 @ A @ D @ E ) @ ( k1_tsep_1 @ A @ B @ C ) ) ) ) )
=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(450,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( k2_tops_2 @ B @ A @ ( k2_tops_2 @ A @ B @ C ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tops_2) ).
thf(4306,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( k2_tops_2 @ B @ A @ ( k2_tops_2 @ A @ B @ C ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(5194,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(2060,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_tsep_1) ).
thf(12480,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060]) ).
thf(1873,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
| ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tex_2) ).
thf(11700,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_xboole_0 @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) ) @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
| ( ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873]) ).
thf(2017,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(12298,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017]) ).
thf(670,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_tex_2) ).
thf(5336,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1973,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r3_tsep_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( E
= ( u1_struct_0 @ C ) ) )
=> ( r1_connsp_1 @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_tsep_1) ).
thf(12125,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( r3_tsep_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( E
= ( u1_struct_0 @ C ) ) )
=> ( r1_connsp_1 @ A @ D @ E ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D
= ( u1_struct_0 @ B ) )
& ( E
= ( u1_struct_0 @ C ) ) )
=> ( r1_connsp_1 @ A @ D @ E ) ) ) )
=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_partfun1) ).
thf(4619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(1407,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(9427,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(1388,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(9321,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(772,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(5864,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(1704,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
<=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tops_3) ).
thf(10909,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) )
=> ( C = D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(1369,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tex_3) ).
thf(9239,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1213,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(8324,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1660,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tex_4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_4) ).
thf(10733,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tex_4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ B @ D ) ) ) )
=> ( v1_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(1753,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ( r2_hidden @ B @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pre_topc) ).
thf(11140,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( r2_hidden @ B @ ( u1_pre_topc @ A ) ) )
& ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(1511,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( k3_tsp_2 @ A @ B )
= ( k1_tsp_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_tsp_2) ).
thf(10041,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( k3_tsp_2 @ A @ B )
= ( k1_tsp_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
= B )
& ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_funct_2) ).
thf(3987,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
= B )
& ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(2012,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_tex_4) ).
thf(12285,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_tex_4 @ A @ B )
= ( k2_tex_4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(4663,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r7_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_binop_1) ).
thf(4597,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r7_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
=> ( r7_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1502,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_tsp_1) ).
thf(9976,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(944,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
<=> ( v3_pre_topc @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(6782,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( v3_pre_topc @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) @ A ) )
& ( ( v3_pre_topc @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) @ A )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(389,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( v1_borsuk_1 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tsep_1) ).
thf(3992,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_borsuk_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( v1_borsuk_1 @ ( k2_tsep_1 @ A @ B @ C ) @ A )
& ( m1_pre_topc @ ( k2_tsep_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1884,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_subset_1) ).
thf(11744,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884]) ).
thf(2040,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_tops_1) ).
thf(12391,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040]) ).
thf(1473,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
=> ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tex_2) ).
thf(9812,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
=> ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v3_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ D )
=> ( r2_hidden @ ( k4_tarski @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_eqrel_1) ).
thf(4039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v3_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ D )
=> ( r2_hidden @ ( k4_tarski @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(1750,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_pre_topc @ B )
=> ~ ( v1_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_tex_2) ).
thf(11131,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v2_pre_topc @ B )
=> ~ ( v1_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(1689,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_pre_topc) ).
thf(10838,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(7081,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(7542,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(2517,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1966,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ( v1_tex_2 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tex_4) ).
thf(12108,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A )
& ( v1_tex_2 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966]) ).
thf(394,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(4014,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(4399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(2097,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tops_1) ).
thf(12658,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ? [C: $i] :
( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( ( v3_relat_2 @ D )
& ( v8_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_eqrel_1) ).
thf(3860,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ? [C: $i] :
( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( ( v3_relat_2 @ D )
& ( v8_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(3785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1081,axiom,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( k5_pcomps_1 @ A )
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pcomps_1) ).
thf(7634,plain,
! [A: $i] :
( ( l1_metric_1 @ A )
=> ( ( k5_pcomps_1 @ A )
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( k4_pcomps_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k5_pre_topc @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_pre_topc) ).
thf(9806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k5_pre_topc @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(1566,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( v1_tops_3 @ B @ A )
<=> ( v3_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_tex_3) ).
thf(10291,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( ( v1_tops_3 @ B @ A )
=> ( v3_tops_1 @ C @ A ) )
& ( ( v3_tops_1 @ C @ A )
=> ( v1_tops_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(1933,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v6_tops_1 @ B @ A )
& ( v6_tops_1 @ C @ A ) )
=> ( v6_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_tops_1) ).
thf(11960,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v6_tops_1 @ B @ A )
& ( v6_tops_1 @ C @ A ) )
=> ( v6_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933]) ).
thf(469,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funcop_1) ).
thf(4378,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funcop_1) ).
thf(3232,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(5971,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1981,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
& ( m1_connsp_2 @ D @ A @ B ) )
=> ( m1_connsp_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_connsp_2) ).
thf(12162,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_connsp_2 @ C @ A @ B )
& ( m1_connsp_2 @ D @ A @ B ) )
=> ( m1_connsp_2 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981]) ).
thf(926,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relset_1) ).
thf(6693,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1368,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc35_tex_2) ).
thf(9229,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ~ ( v1_borsuk_1 @ B @ A )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(3291,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1240,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A )
& ( v1_tops_3 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= B )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_3) ).
thf(8478,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tops_1 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ( v2_tops_1 @ C @ A )
& ( v1_tops_3 @ D @ A )
& ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= B )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D )
= ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(950,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ( v3_pre_topc @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tex_3) ).
thf(6822,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_1 @ B @ A )
& ( v3_pre_topc @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v1_tsep_1 @ C @ A )
& ( v2_tex_2 @ C @ A )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(758,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ C )
<=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_t_0topsp) ).
thf(5796,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ C )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ C ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(462,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_binop_1) ).
thf(4356,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v1_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) )
=> ( v1_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1543,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v2_t_0topsp @ A )
<=> ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ( r2_hidden @ C @ D )
& ~ ( r2_hidden @ B @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_t_0topsp) ).
thf(10173,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ( v2_t_0topsp @ A )
=> ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ( r2_hidden @ C @ D )
& ~ ( r2_hidden @ B @ D ) ) ) ) ) ) ) ) ) )
& ( ( ( v3_struct_0 @ A )
| ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ( r2_hidden @ C @ D )
& ~ ( r2_hidden @ B @ D ) ) ) ) ) ) ) ) )
=> ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc34_membered) ).
thf(3601,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(2035,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_tops_1) ).
thf(12374,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035]) ).
thf(1207,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ B @ D )
= ( k3_xboole_0 @ ( k6_pre_topc @ A @ C ) @ ( k2_pre_topc @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_pre_topc) ).
thf(8296,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ B @ D )
= ( k3_xboole_0 @ ( k6_pre_topc @ A @ C ) @ ( k2_pre_topc @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1845,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ( v2_borsuk_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v6_compts_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_borsuk_1) ).
thf(11589,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ( ( v2_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v6_compts_1 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v6_compts_1 @ C @ A ) ) )
=> ( v2_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).
thf(1633,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ C )
& ( v4_pre_topc @ C @ A ) )
=> ( C
= ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_3) ).
thf(10601,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ C )
& ( v4_pre_topc @ C @ A ) )
=> ( C
= ( u1_struct_0 @ A ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ C )
& ( v4_pre_topc @ C @ A ) )
=> ( C
= ( u1_struct_0 @ A ) ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(369,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(3892,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1600,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tops_1) ).
thf(10443,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_partfun1) ).
thf(2522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_partfun1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_2) ).
thf(3373,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_partfun1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1052,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
<=> ( r3_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tsep_1) ).
thf(7489,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( r1_tsep_1 @ A @ B @ C )
=> ( r3_tsep_1 @ A @ B @ C ) )
& ( ( r3_tsep_1 @ A @ B @ C )
=> ( r1_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1099,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(7712,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1422,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(9523,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(1775,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(11219,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).
thf(5078,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(566,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(4843,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(303,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(3521,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(1911,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m1_connsp_2 @ F @ B @ D )
=> ( m1_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k8_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_borsuk_1) ).
thf(11843,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m1_connsp_2 @ F @ B @ D )
=> ( m1_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k8_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ? [C: $i] :
( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( B
= ( k7_eqrel_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_eqrel_1) ).
thf(2736,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ? [C: $i] :
( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( B
= ( k7_eqrel_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(2014,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k3_pcomps_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pcomps_1) ).
thf(12292,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k3_pcomps_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014]) ).
thf(1002,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(7121,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(2105,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k3_borsuk_1 @ A @ B @ C )
= ( k1_borsuk_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_borsuk_1) ).
thf(12681,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k3_borsuk_1 @ A @ B @ C )
= ( k1_borsuk_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105]) ).
thf(1797,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_3_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v1_tex_4 @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_tex_4) ).
thf(11341,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v1_tex_4 @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v1_tex_4 @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_3_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).
thf(966,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v4_tex_3 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tex_3) ).
thf(6906,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v4_tex_3 @ B @ A ) )
& ( v3_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1853,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tex_2 @ B @ A )
<=> ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tex_2) ).
thf(11612,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_tex_2 @ B @ A )
=> ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v4_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).
thf(337,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funcop_1) ).
thf(3690,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(841,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( ( r4_tsep_1 @ A @ B @ C )
<=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ~ ( ( A
!= ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_tsep_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( A
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ F @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_tsep_1) ).
thf(6226,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( ( ( r4_tsep_1 @ A @ B @ C )
=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ~ ( ( A
!= ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_tsep_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( A
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ F @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) )
& ( ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_borsuk_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_borsuk_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ~ ( ( A
!= ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_tsep_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( A
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ F @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1269,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(8621,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(3164,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1682,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tops_1) ).
thf(10804,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_funct_2) ).
thf(4474,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(1888,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v2_tops_1 @ D @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tops_3) ).
thf(11759,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v2_tops_1 @ D @ B ) )
=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(7323,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1647,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tex_2) ).
thf(10649,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(1102,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_tex_3) ).
thf(7727,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(4029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(909,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k15_borsuk_1 @ A ) )
& ( v1_setfam_1 @ ( k15_borsuk_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_borsuk_1) ).
thf(6627,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k15_borsuk_1 @ A ) )
& ( v1_setfam_1 @ ( k15_borsuk_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1413,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc26_tex_3) ).
thf(9466,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(4777,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(403,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4051,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1773,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(11214,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(1768,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tsp_1) ).
thf(11199,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(1248,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_xboole_1) ).
thf(8521,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1837,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i,D: $i] :
( ( ( g1_pre_topc @ A @ B )
= ( g1_pre_topc @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(11557,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i,D: $i] :
( ( ( g1_pre_topc @ A @ B )
= ( g1_pre_topc @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( k1_tsep_1 @ A @ B @ C )
= ( k1_tsep_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k1_tsep_1) ).
thf(6294,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( k1_tsep_1 @ A @ B @ C )
= ( k1_tsep_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_partfun1) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(4286,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(1766,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_borsuk_1) ).
thf(11194,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(1541,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tops_1) ).
thf(10168,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(1588,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v1_tsp_1 @ B @ A ) )
=> ( v1_tsp_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tsp_1) ).
thf(10379,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v1_tsp_1 @ B @ A ) )
=> ( v1_tsp_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(1247,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc31_tex_2) ).
thf(8510,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v4_ordinal2 @ A )
& ( v4_ordinal2 @ B )
& ( v4_ordinal2 @ C ) )
=> ( ( v1_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v2_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v3_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v4_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v5_membered @ ( k1_enumset1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc21_membered) ).
thf(4968,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v4_ordinal2 @ A )
& ( v4_ordinal2 @ B )
& ( v4_ordinal2 @ C ) )
=> ( ( v1_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v2_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v3_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v4_membered @ ( k1_enumset1 @ A @ B @ C ) )
& ( v5_membered @ ( k1_enumset1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(933,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( v1_realset1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tex_2) ).
thf(6735,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1858,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v3_compts_1 @ A )
& ( v2_pcomps_1 @ A ) )
=> ( v4_compts_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_pcomps_1) ).
thf(11627,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( ( v3_compts_1 @ A )
& ( v2_pcomps_1 @ A ) )
=> ( v4_compts_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858]) ).
thf(2122,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tsep_1) ).
thf(12734,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122]) ).
thf(293,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v2_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_binop_1) ).
thf(3479,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v2_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) )
=> ( v2_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(1497,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k6_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) )
& ~ ( v2_tex_2 @ ( k6_tex_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc18_tex_4) ).
thf(9959,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k6_tex_4 @ A @ B ) )
& ( v1_pre_topc @ ( k6_tex_4 @ A @ B ) )
& ~ ( v2_tex_2 @ ( k6_tex_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(711,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(5564,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v2_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v1_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v2_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v4_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v5_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_realset2 @ ( k1_tex_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tex_2) ).
thf(8395,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k1_tex_2 @ A @ B ) )
& ( v1_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v2_pre_topc @ ( k1_tex_2 @ A @ B ) )
& ( v1_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v2_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v4_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v5_tdlat_3 @ ( k1_tex_2 @ A @ B ) )
& ( v3_realset2 @ ( k1_tex_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1480,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(9874,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1382,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_tex_2) ).
thf(9299,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(849,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_pre_topc) ).
thf(6287,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(2140,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_pre_topc) ).
thf(12801,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140]) ).
thf(939,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_tex_3) ).
thf(6765,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1461,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tex_3) ).
thf(9752,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v1_borsuk_1 @ C @ A )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1771,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
| ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tops_3) ).
thf(11209,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
| ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(1734,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
=> ( r2_tsep_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tsep_1) ).
thf(11067,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
=> ( r2_tsep_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ D ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r5_binop_1 @ A @ C @ B )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_binop_1) ).
thf(2404,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r5_binop_1 @ A @ C @ B )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(962,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tex_3) ).
thf(6889,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v1_tops_3 @ B @ A )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v2_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( B
!= ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1794,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(11326,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
<=> ( ( k2_relat_1 @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
=> ( ( k2_relat_1 @ C )
= B ) )
& ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(2120,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_tex_2) ).
thf(12729,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tex_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ ( k1_struct_0 @ A @ C ) ) )
= ( k1_struct_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120]) ).
thf(679,axiom,
! [A: $i] :
( ( ( v1_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k3_pre_topc @ A @ ( k2_pre_topc @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_tsep_1) ).
thf(5378,plain,
! [A: $i] :
( ( ( v1_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k3_pre_topc @ A @ ( k2_pre_topc @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1868,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_7_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_7_tex_4) ).
thf(11668,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_7_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( v3_pre_topc @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_7_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868]) ).
thf(1469,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ~ ( v2_t_0topsp @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_tsp_1) ).
thf(9795,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v2_t_0topsp @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ~ ( v2_t_0topsp @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1204,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ F @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tsep_1) ).
thf(8268,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
=> ( ( ( r2_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ F @ A ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ F @ A ) ) ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(2223,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(922,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v5_pre_topc @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_pre_topc @ A @ B @ C @ ( k6_pre_topc @ A @ D ) ) @ ( k6_pre_topc @ B @ ( k4_pre_topc @ A @ B @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tops_2) ).
thf(6682,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v5_pre_topc @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_pre_topc @ A @ B @ C @ ( k6_pre_topc @ A @ D ) ) @ ( k6_pre_topc @ B @ ( k4_pre_topc @ A @ B @ C @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_pre_topc @ A @ B @ C @ ( k6_pre_topc @ A @ D ) ) @ ( k6_pre_topc @ B @ ( k4_pre_topc @ A @ B @ C @ D ) ) ) )
=> ( v5_pre_topc @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1894,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_tops_3) ).
thf(11776,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(5642,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(869,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc22_tex_3) ).
thf(6398,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1816,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(11422,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(4193,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1381,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tex_2) ).
thf(9293,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v5_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_pre_topc @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(1949,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ C ) @ ( k6_pre_topc @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_tops_3) ).
thf(12022,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ C ) @ ( k6_pre_topc @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k2_tops_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_tops_2 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k2_tops_2 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tops_2) ).
thf(7291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_struct_0 @ A )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k2_tops_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_tops_2 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k2_tops_2 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(2057,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( u1_struct_0 @ A ) )
=> ( ( v3_tex_2 @ B @ A )
<=> ( v1_tdlat_3 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tex_2) ).
thf(12466,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( u1_struct_0 @ A ) )
=> ( ( ( v3_tex_2 @ B @ A )
=> ( v1_tdlat_3 @ A ) )
& ( ( v1_tdlat_3 @ A )
=> ( v3_tex_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057]) ).
thf(198,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( ( k1_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D )
= ( k2_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ D ) @ ( k1_tsep_1 @ A @ C @ D ) ) )
& ( ( k1_tsep_1 @ A @ D @ ( k2_tsep_1 @ A @ B @ C ) )
= ( k2_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ B ) @ ( k1_tsep_1 @ A @ D @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tsep_1) ).
thf(3045,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( m1_pre_topc @ D @ A ) )
=> ( ~ ( r1_tsep_1 @ A @ B @ C )
=> ( ( ( k1_tsep_1 @ A @ ( k2_tsep_1 @ A @ B @ C ) @ D )
= ( k2_tsep_1 @ A @ ( k1_tsep_1 @ A @ B @ D ) @ ( k1_tsep_1 @ A @ C @ D ) ) )
& ( ( k1_tsep_1 @ A @ D @ ( k2_tsep_1 @ A @ B @ C ) )
= ( k2_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ B ) @ ( k1_tsep_1 @ A @ D @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(3673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_membered) ).
thf(6309,plain,
! [A: $i,B: $i] :
( ( v1_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_partfun1) ).
thf(5110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(2051,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tops_3) ).
thf(12444,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051]) ).
thf(1398,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_tex_3) ).
thf(9382,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A )
& ~ ( v2_tex_3 @ B @ A )
& ( v3_tex_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2783,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1675,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_tops_1 @ B @ A )
<=> ( B
= ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_tops_1) ).
thf(10781,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v6_tops_1 @ B @ A )
=> ( B
= ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) ) )
& ( ( B
= ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
=> ( v6_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(1551,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
<=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tops_3) ).
thf(10224,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( u1_struct_0 @ A ) ) )
& ( ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( u1_struct_0 @ A ) )
=> ( v1_tops_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(1964,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_tops_1) ).
thf(12102,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964]) ).
thf(845,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ~ ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tsp_1) ).
thf(6269,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ~ ( v2_t_0topsp @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r3_binop_1 @ A @ B @ C )
<=> ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_binop_1) ).
thf(2549,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r3_binop_1 @ A @ B @ C )
=> ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) ) )
& ( ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) )
=> ( r3_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1521,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pcomps_1 @ B @ A )
=> ( v1_pcomps_1 @ ( k3_pcomps_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_pcomps_1) ).
thf(10092,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pcomps_1 @ B @ A )
=> ( v1_pcomps_1 @ ( k3_pcomps_1 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(1133,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc46_tex_2) ).
thf(7925,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v5_tex_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v3_realset2 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1780,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( v1_tex_3 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_tex_3) ).
thf(11236,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( m1_pre_topc @ B @ C )
=> ( ( v1_tex_3 @ B @ C )
& ( m1_pre_topc @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(2810,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(627,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v4_membered @ B ) )
=> ( v4_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_membered) ).
thf(5151,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v4_membered @ B ) )
=> ( v4_membered @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(103,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(2583,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
= ( k6_partfun1 @ B ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_2) ).
thf(4019,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
= ( k6_partfun1 @ B ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1945,axiom,
m1_subset_1 @ k23_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_borsuk_1) ).
thf(12007,plain,
m1_subset_1 @ k23_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).
thf(83,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( r2_hidden @ B @ A ) )
=> ( A = k5_numbers ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_membered) ).
thf(2502,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( r2_hidden @ B @ A ) )
=> ( A = k5_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( k3_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k6_domain_1 @ ( k2_zfmisc_1 @ B @ C ) @ ( k1_domain_1 @ B @ C @ E @ F ) ) )
= ( k12_mcart_1 @ A @ C @ ( k3_funct_2 @ A @ B @ D @ ( k6_domain_1 @ B @ E ) ) @ ( k6_domain_1 @ C @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_borsuk_1) ).
thf(2241,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( k3_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k6_domain_1 @ ( k2_zfmisc_1 @ B @ C ) @ ( k1_domain_1 @ B @ C @ E @ F ) ) )
= ( k12_mcart_1 @ A @ C @ ( k3_funct_2 @ A @ B @ D @ ( k6_domain_1 @ B @ E ) ) @ ( k6_domain_1 @ C @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1015,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(7214,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(4848,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(2966,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(2047,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(12435,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).
thf(63,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
thf(2430,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(815,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tdlat_3 @ B )
=> ( v3_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_tex_2) ).
thf(6099,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tdlat_3 @ B )
=> ( v3_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1144,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7987,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(7227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1856,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_tex_4) ).
thf(11621,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ ( k6_pre_topc @ A @ B ) )
& ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856]) ).
thf(107,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(2600,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1996,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ B @ C )
& ( v4_tex_2 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tex_2) ).
thf(12220,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_tex_2 @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ B @ C )
& ( v4_tex_2 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).
thf(1055,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(7506,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1727,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v3_tex_2 @ B @ A ) )
=> ( v3_pre_topc @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tex_2) ).
thf(11050,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
& ( v3_tex_2 @ B @ A ) )
=> ( v3_pre_topc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(1932,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ( ( r1_tarski @ B @ C )
=> ( m2_connsp_2 @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_borsuk_1) ).
thf(11958,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ( ( r1_tarski @ B @ C )
=> ( m2_connsp_2 @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(5637,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1713,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] : ( m1_connsp_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(10988,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] : ( m1_connsp_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(982,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc40_tex_2) ).
thf(6993,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tex_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1561,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_tops_3) ).
thf(10255,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(1801,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_3) ).
thf(11358,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).
thf(1415,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(9474,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(714,axiom,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(5581,plain,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(837,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(6209,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
= ( k3_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).
thf(4876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
= ( k3_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(1421,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( m1_tsp_1 @ B @ A )
<=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_pre_topc @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tsp_1) ).
thf(9504,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( m1_tsp_1 @ B @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) )
=> ( v3_pre_topc @ C @ B ) ) ) ) ) )
& ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( C
= ( k3_xboole_0 @ D @ ( u1_struct_0 @ B ) ) ) )
=> ( v3_pre_topc @ C @ B ) ) ) ) )
=> ( m1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(8093,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(1431,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(9583,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(5280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1458,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(9737,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(3817,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(383,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( A
= ( k2_zfmisc_1 @ B @ C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( ( k1_relat_1 @ A )
= B )
& ( ( k2_relat_1 @ A )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funcop_1) ).
thf(3965,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( A
= ( k2_zfmisc_1 @ B @ C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( ( k1_relat_1 @ A )
= B )
& ( ( k2_relat_1 @ A )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1287,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
<=> ( ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tex_3) ).
thf(8730,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
=> ( ( ( ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ( ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) )
& ( ( ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( v3_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(3020,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1362,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc30_tex_3) ).
thf(9193,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1098,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( v1_tex_3 @ B @ A ) )
=> ( v1_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tex_3) ).
thf(7708,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ( ! [B: $i] :
( ( ( v2_tex_2 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ~ ( v1_tex_3 @ B @ A ) )
=> ( v1_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(84,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funcop_1) ).
thf(2507,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1038,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc16_tex_2) ).
thf(7370,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_tsep_1 @ B @ A )
& ( v1_borsuk_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(5958,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(275,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(3392,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(987,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
<=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tops_3) ).
thf(7025,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_pre_topc @ A ) ) )
& ( ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_pre_topc @ A ) )
=> ( v1_tops_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1570,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k1_tops_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_2) ).
thf(10308,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k1_tops_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_pre_topc @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(436,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C )
= ( k3_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_borsuk_1) ).
thf(4229,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C )
= ( k3_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1691,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_tops_3) ).
thf(10845,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ C @ D )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v1_tops_1 @ C @ A ) )
=> ( v1_tops_1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(6595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1109,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(7755,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(1817,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ D )
| ( r1_connsp_1 @ A @ C @ D ) )
=> ( r1_connsp_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tsep_1) ).
thf(11425,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_connsp_1 @ A @ B @ D )
| ( r1_connsp_1 @ A @ C @ D ) )
=> ( r1_connsp_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817]) ).
thf(534,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(4659,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
& ( ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(546,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(4713,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(1079,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_1 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ F @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tsep_1) ).
thf(7617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ F @ A ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ B )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ E @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ C )
& ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ F @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( ( u1_struct_0 @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( v3_pre_topc @ D @ A )
& ( v3_pre_topc @ E @ A )
& ( v4_pre_topc @ F @ A ) ) ) )
=> ( r2_tsep_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1236,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v4_tex_4 @ B @ A )
<=> ( ( v2_tdlat_3 @ B )
& ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v2_tdlat_3 @ C )
& ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_tex_4) ).
thf(8453,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v4_tex_4 @ B @ A )
=> ( ( v2_tdlat_3 @ B )
& ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v2_tdlat_3 @ C )
& ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) ) ) ) ) )
& ( ( ( v2_tdlat_3 @ B )
& ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( v2_tdlat_3 @ C )
& ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) ) ) ) )
=> ( v4_tex_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1575,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tops_1) ).
thf(10323,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4395,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1644,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
| ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tops_3) ).
thf(10642,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_3 @ B @ A )
| ( v1_tops_3 @ C @ A ) )
=> ( v1_tops_3 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(779,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ D @ C )
<=> ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) ) ) )
& ( ( k6_pre_topc @ A @ B )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pre_topc) ).
thf(5891,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) ) )
& ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ( k6_pre_topc @ A @ B )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1503,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k11_borsuk_1 @ A @ B @ C )
= ( a_3_1_borsuk_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_borsuk_1) ).
thf(9979,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k11_borsuk_1 @ A @ B @ C )
= ( a_3_1_borsuk_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(157,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(2864,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1344,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_relat_1 @ ( k17_borsuk_1 @ A @ B ) )
= ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_borsuk_1) ).
thf(9066,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_relat_1 @ ( k17_borsuk_1 @ A @ B ) )
= ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_2) ).
thf(3076,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(210,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_membered) ).
thf(3113,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(897,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ~ ( v2_tex_2 @ B @ A )
& ( v5_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc24_tex_3) ).
thf(6548,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_tex_3 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A )
& ( v1_tsep_1 @ B @ A )
& ( v1_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ~ ( v2_tex_2 @ B @ A )
& ( v5_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_3 @ B @ A )
& ~ ( v3_tex_3 @ B @ A )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1013,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( ( r4_tsep_1 @ A @ B @ C )
<=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ~ ( ( A
!= ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_borsuk_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( A
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ F @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_tsep_1) ).
thf(7176,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( A
= ( k1_tsep_1 @ A @ B @ C ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( ( ( r4_tsep_1 @ A @ B @ C )
=> ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ~ ( ( A
!= ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_borsuk_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( A
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ F @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) ) )
& ( ~ ( ~ ( m1_pre_topc @ B @ C )
& ~ ( m1_pre_topc @ C @ B )
& ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v1_tsep_1 @ D @ A )
& ( m1_pre_topc @ D @ A ) )
=> ! [E: $i] :
( ( ~ ( v3_struct_0 @ E )
& ( v1_tsep_1 @ E @ A )
& ( m1_pre_topc @ E @ A ) )
=> ~ ( ( m1_pre_topc @ D @ B )
& ( m1_pre_topc @ E @ C )
& ~ ( ( A
!= ( k1_tsep_1 @ A @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v1_borsuk_1 @ F @ A )
& ( m1_pre_topc @ F @ A ) )
=> ~ ( ( A
= ( k1_tsep_1 @ A @ ( k1_tsep_1 @ A @ D @ E ) @ F ) )
& ( m1_pre_topc @ F @ ( k2_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ) )
=> ( r4_tsep_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r5_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_binop_1) ).
thf(2484,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r5_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(727,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ! [C: $i] :
( ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) )
=> ( v2_tdlat_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tex_4) ).
thf(5645,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ! [C: $i] :
( ( ( v1_tsep_1 @ C @ A )
& ( m1_pre_topc @ C @ A ) )
=> ( ( r1_tsep_1 @ A @ B @ C )
| ( m1_pre_topc @ B @ C ) ) )
=> ( v2_tdlat_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_2) ).
thf(7252,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(414,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v8_relat_2 @ A )
<=> ( r1_tarski @ ( k5_relat_1 @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_2) ).
thf(4088,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v8_relat_2 @ A )
=> ( r1_tarski @ ( k5_relat_1 @ A @ A ) @ A ) )
& ( ( r1_tarski @ ( k5_relat_1 @ A @ A ) @ A )
=> ( v8_relat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(1021,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tex_3) ).
thf(7246,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ~ ( v1_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tex_2 @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ? [C: $i] :
( ~ ( v3_struct_0 @ C )
& ( v1_pre_topc @ C )
& ( v3_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A )
& ( r4_tsep_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(4363,plain,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1310,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pre_topc) ).
thf(8857,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ~ ( ? [C: $i] : ( r2_hidden @ C @ A )
& ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_eqrel_1) ).
thf(2372,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ~ ( ? [C: $i] : ( r2_hidden @ C @ A )
& ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1819,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).
thf(11430,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).
thf(1976,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v1_pcomps_1 @ C @ A ) )
=> ( v1_pcomps_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pcomps_1) ).
thf(12144,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( v1_pcomps_1 @ C @ A ) )
=> ( v1_pcomps_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(5344,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(261,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc25_tex_3) ).
thf(3341,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v4_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1787,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_2 @ B @ A )
<=> ( ( v1_tsp_1 @ B @ A )
& ( ( k3_tex_4 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tsp_2) ).
thf(11298,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_2 @ B @ A )
=> ( ( v1_tsp_1 @ B @ A )
& ( ( k3_tex_4 @ A @ B )
= ( u1_struct_0 @ A ) ) ) )
& ( ( ( v1_tsp_1 @ B @ A )
& ( ( k3_tex_4 @ A @ B )
= ( u1_struct_0 @ A ) ) )
=> ( v1_tsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(777,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc36_tex_2) ).
thf(5877,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tdlat_3 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v1_tdlat_3 @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ( v3_realset2 @ B )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1529,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( v3_tex_3 @ B @ A )
<=> ( v2_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tex_3) ).
thf(10118,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( ( ( v3_tex_3 @ B @ A )
=> ( v2_tops_1 @ C @ A ) )
& ( ( v2_tops_1 @ C @ A )
=> ( v3_tex_3 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(2866,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(956,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v3_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_tex_3) ).
thf(6857,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v1_tsep_1 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v3_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1886,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_pre_topc) ).
thf(11754,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886]) ).
thf(596,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(4977,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(5,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(2191,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1943,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tsp_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( C = D )
| ( r1_subset_1 @ ( k4_tex_4 @ A @ C ) @ ( k4_tex_4 @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tsp_2) ).
thf(11990,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( C = D )
| ( r1_subset_1 @ ( k4_tex_4 @ A @ C ) @ ( k4_tex_4 @ A @ D ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( C = D )
| ( r1_subset_1 @ ( k4_tex_4 @ A @ C ) @ ( k4_tex_4 @ A @ D ) ) ) ) ) )
=> ( v1_tsp_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(3960,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1429,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc44_tex_2) ).
thf(9568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v2_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ~ ( v3_realset2 @ B ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( v2_tdlat_3 @ B )
& ( v3_tdlat_3 @ B )
& ( v4_tdlat_3 @ B )
& ( v5_tdlat_3 @ B )
& ~ ( v5_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( ( v2_membered @ A )
& ( v2_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc23_membered) ).
thf(3474,plain,
! [A: $i,B: $i] :
( ( ( v2_membered @ A )
& ( v2_membered @ B ) )
=> ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1590,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v1_tex_4 @ C @ A ) )
=> ( v1_tex_4 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_tex_4) ).
thf(10383,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v1_tex_4 @ C @ A ) )
=> ( v1_tex_4 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(1294,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
& ( v1_tdlat_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tex_3) ).
thf(8786,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ( v1_tex_3 @ B @ A )
& ( v2_tex_2 @ B @ A ) )
& ( v1_tdlat_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(852,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(6297,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(116,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k1_binop_1 @ A @ B @ C )
= ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(2672,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k1_binop_1 @ A @ B @ C )
= ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(2879,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_membered) ).
thf(3950,plain,
! [A: $i,B: $i] :
( ( v5_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(1978,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k3_t_0topsp @ A ) )
& ( v2_pre_topc @ ( k3_t_0topsp @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_t_0topsp) ).
thf(12149,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k3_t_0topsp @ A ) )
& ( v2_pre_topc @ ( k3_t_0topsp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( r1_partfun1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_partfun1) ).
thf(3437,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( r1_partfun1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(6961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(497,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ ( k2_tops_2 @ A @ B @ C ) )
= ( k2_pre_topc @ B ) )
& ( ( k2_relat_1 @ ( k2_tops_2 @ A @ B @ C ) )
= ( k2_pre_topc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tops_2) ).
thf(4520,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k2_pre_topc @ B ) )
& ( v2_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ ( k2_tops_2 @ A @ B @ C ) )
= ( k2_pre_topc @ B ) )
& ( ( k2_relat_1 @ ( k2_tops_2 @ A @ B @ C ) )
= ( k2_pre_topc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(578,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(4891,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1709,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
<=> ( v1_tops_3 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tops_3) ).
thf(10934,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( v1_tops_3 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v1_tops_3 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(1557,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(10245,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(4723,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1581,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_tsp_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_tsp_1) ).
thf(10344,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_tsp_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(4949,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(556,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v5_membered @ B ) )
=> ( v5_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_membered) ).
thf(4767,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v5_membered @ B ) )
=> ( v5_membered @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1467,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k2_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tops_2) ).
thf(9784,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k2_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ( v4_ordinal2 @ A )
& ( v4_ordinal2 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) )
& ( v4_membered @ ( k2_tarski @ A @ B ) )
& ( v5_membered @ ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_membered) ).
thf(2690,plain,
! [A: $i,B: $i] :
( ( ( v4_ordinal2 @ A )
& ( v4_ordinal2 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) )
& ( v4_membered @ ( k2_tarski @ A @ B ) )
& ( v5_membered @ ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1860,axiom,
l1_pre_topc @ k22_borsuk_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_borsuk_1) ).
thf(11631,plain,
l1_pre_topc @ k22_borsuk_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).
thf(1941,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( v2_tops_1 @ B @ A )
<=> ( v1_tops_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_tex_3) ).
thf(11985,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_tsep_2 @ A @ B @ C )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( v1_tops_1 @ C @ A ) )
& ( ( v1_tops_1 @ C @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941]) ).
thf(979,axiom,
! [A: $i] :
( ( u1_pre_topc @ ( k2_pcomps_1 @ A ) )
= ( k1_pcomps_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_pcomps_1) ).
thf(6984,plain,
! [A: $i] :
( ( u1_pre_topc @ ( k2_pcomps_1 @ A ) )
= ( k1_pcomps_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(691,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
& ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
!= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ F @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tsep_1) ).
thf(5436,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( u1_struct_0 @ A ) )
& ( r2_tsep_1 @ A @ B @ C )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( v4_pre_topc @ E @ A )
& ( r1_tarski @ D @ B )
& ( r1_tarski @ E @ C )
& ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
!= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
& ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ E ) @ F ) )
& ( r1_tarski @ F @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( v3_pre_topc @ F @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1700,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
=> ( v1_tops_3 @ ( k1_tops_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tops_3) ).
thf(10900,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_3 @ B @ A )
=> ( v1_tops_3 @ ( k1_tops_1 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(1121,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v3_tex_3 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tex_3) ).
thf(7861,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( v2_tops_1 @ B @ A )
& ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ~ ( ( v3_tex_3 @ C @ A )
& ( B
= ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1782,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tex_3 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ~ ( v3_struct_0 @ C )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_tex_3) ).
thf(11241,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_tex_3 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v1_tex_3 @ C @ B )
& ( m1_pre_topc @ C @ B ) )
=> ( ~ ( v3_struct_0 @ C )
& ( v1_tex_3 @ C @ A )
& ( m1_pre_topc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(1701,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k1_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tex_4) ).
thf(10902,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_tex_4 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k1_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(2063,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v3_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(12488,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v3_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_partfun1) ).
thf(2297,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(66,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_relat_1) ).
thf(2438,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(18,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_2 @ A )
& ( v8_relat_2 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_relat_2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(2238,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_2 @ A )
& ( v8_relat_2 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_relat_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1460,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_metric_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_pcomps_1 @ A ) )
& ( v1_pre_topc @ ( k5_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k5_pcomps_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_pcomps_1) ).
thf(9748,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_metric_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_pcomps_1 @ A ) )
& ( v1_pre_topc @ ( k5_pcomps_1 @ A ) )
& ( v2_pre_topc @ ( k5_pcomps_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1726,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ D )
& ( r2_tsep_1 @ A @ C @ D ) )
=> ( r2_tsep_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tsep_1) ).
thf(11048,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_tsep_1 @ A @ B @ D )
& ( r2_tsep_1 @ A @ C @ D ) )
=> ( r2_tsep_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(4056,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(923,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(6686,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_relat_1) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc35_membered) ).
thf(3637,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1663,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ D @ C )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_tops_3) ).
thf(10745,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_tarski @ D @ C )
& ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(731,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tex_4) ).
thf(5664,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tdlat_3 @ B )
& ~ ( v4_tex_4 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A )
& ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(42,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2351,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1222,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_borsuk_1) ).
thf(8380,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(1960,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k4_tex_4 @ A @ C ) )
<=> ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ ( k4_tex_4 @ A @ B ) @ D )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ C ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ B ) )
& ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tex_4) ).
thf(12070,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k4_tex_4 @ A @ C ) )
=> ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ ( k4_tex_4 @ A @ B ) @ D )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ C ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ B ) )
& ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ D ) ) ) ) )
& ( ~ ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ ( k4_tex_4 @ A @ B ) @ D )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ C ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ D @ A )
& ( r1_xboole_0 @ D @ ( k4_tex_4 @ A @ B ) )
& ( r1_tarski @ ( k4_tex_4 @ A @ C ) @ D ) ) ) )
=> ( r1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k4_tex_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960]) ).
thf(1374,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(9254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(6739,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k14_borsuk_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_borsuk_1) ).
thf(7295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k14_borsuk_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1299,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(8818,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1665,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_pre_topc @ A @ B )
& ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
thf(10750,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_pre_topc @ A @ B )
& ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k19_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k19_borsuk_1) ).
thf(8405,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k19_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).
thf(6948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1864,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_6_tex_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_tex_4 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_6_tex_4) ).
thf(11648,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_6_tex_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_tex_4 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_tex_4 @ B @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_6_tex_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).
thf(1926,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( v4_pre_topc @ D @ B )
& ( D
= ( k3_xboole_0 @ C @ ( u1_struct_0 @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_tsp_1) ).
thf(11896,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m2_tsp_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v4_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( v4_pre_topc @ D @ B )
& ( D
= ( k3_xboole_0 @ C @ ( u1_struct_0 @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( v1_funct_1 @ ( k1_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A )
& ( m2_relset_1 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_borsuk_1) ).
thf(5911,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( v1_funct_1 @ ( k1_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A )
& ( m2_relset_1 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v2_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_membered) ).
thf(2980,plain,
! [A: $i,B: $i] :
( ( v2_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v2_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(197,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(3035,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2022,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
<=> ( m1_pre_topc @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_tsep_1) ).
thf(12316,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_pre_topc @ C @ A )
=> ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( m1_pre_topc @ B @ C ) )
& ( ( m1_pre_topc @ B @ C )
=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).
thf(963,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_borsuk_1) ).
thf(6896,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1954,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_tex_2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tex_2) ).
thf(12047,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( v3_tdlat_3 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_tex_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954]) ).
thf(1523,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v1_tsp_2 @ C @ A ) )
=> ( v1_tsp_2 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_tsp_2) ).
thf(10096,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
= ( g1_pre_topc @ ( u1_struct_0 @ B ) @ ( u1_pre_topc @ B ) ) )
& ( C = D )
& ( v1_tsp_2 @ C @ A ) )
=> ( v1_tsp_2 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(37903,plain,
$false,
inference(cvc4,[status(thm)],[8536,10647,4094,4909,5136,12526,10520,5320,2463,2559,6845,12738,9982,9131,6085,10917,8618,8930,4560,10609,8186,5116,10410,12055,5088,9273,12597,6669,6355,12057,12490,4450,9786,5857,2341,11372,4062,2263,12116,4729,4022,12189,11504,10730,3477,11581,4852,10743,6431,5676,6317,2427,10944,12383,5778,10319,6690,8415,11763,4682,8475,8887,11394,11385,9091,8828,10790,12689,12549,10507,3534,10234,12172,5297,6441,3108,2837,9759,7813,10387,11224,5898,11308,7888,4376,11350,9621,8450,8129,2940,7935,5141,12094,5225,4226,11635,6162,9351,7008,4311,5696,9924,2644,3230,5292,7958,9604,2908,5842,9456,6619,11353,10711,6338,6830,5982,9059,8169,5669,5265,12789,7781,4614,2854,8563,10294,10125,10039,9400,4408,6602,5383,6214,9003,6194,9933,5361,3942,10346,11962,12545,10827,5708,8012,3848,3017,4543,8101,4633,3439,9526,9460,11072,4418,4739,9127,6939,12847,5589,8150,7697,7695,10103,7405,5755,3648,7556,2918,4220,4528,3175,10864,9565,2448,5257,4638,3693,6078,4650,2476,7147,11239,9356,10170,5782,9246,7980,11756,10341,12816,9481,9774,3276,3370,4679,9379,3281,9657,7592,5024,11171,10662,10336,9476,3350,5740,10923,12686,3766,2432,7637,3915,5935,11382,8539,11907,6381,11568,6872,4266,12212,10545,11863,2886,5903,8122,3809,12339,4607,9148,10559,2516,12785,6608,9013,6291,12661,3597,7311,2869,10248,10142,8214,12417,9938,12869,3820,5553,5953,9447,9056,7241,3221,4546,9989,2603,3195,9172,11976,5306,4866,4563,12943,6039,9410,10587,7825,9828,12122,9597,6538,3131,11203,4070,7401,10997,8225,2339,11025,9561,11817,4415,7822,6987,3495,10251,12718,11010,6423,11087,12154,2708,4654,3617,10221,6350,2217,3653,10719,8834,2274,12394,12901,5130,3410,7867,2185,5160,11812,9909,8208,5182,8146,12606,9668,6434,5989,6519,7000,4568,3353,5836,2745,12713,2571,8753,8748,6130,8235,5746,4471,8252,9877,8907,2713,3517,3998,3840,5355,3463,12920,5868,3385,12837,4353,5866,5214,5605,11331,8902,12804,4617,6611,7124,12319,10110,11564,9941,6579,10074,11247,12642,4622,6272,5397,5622,11802,10206,12229,11115,11600,2929,6923,4551,12864,5829,3014,2730,8384,9869,7965,6025,8558,5617,7509,7309,3258,12782,8870,10764,9266,7733,11740,11533,8293,10497,2829,4595,12185,9103,8229,5013,12593,6187,12237,7532,8526,2178,5682,4411,10046,10454,4696,4205,5433,9304,11821,11314,8956,9593,7492,11778,4329,12706,11656,3199,4857,10623,2996,9088,4454,11500,10626,6657,8158,4001,3527,11154,3702,3983,6534,7376,12296,12105,10757,10085,10786,5650,8018,5311,5985,4871,4783,9781,9319,12379,6717,8196,3851,12888,11036,8411,9309,11632,11168,10799,9928,8823,11136,10106,2750,3906,3389,12090,12330,12504,5929,12678,11312,7036,3537,9897,6648,8595,8727,5220,5210,9970,6755,12311,6777,5096,11119,3421,5370,10538,12777,11413,12008,9035,5169,12499,10350,9341,9187,10895,3955,11408,4701,12860,5489,6327,11596,8443,11143,6616,6787,4211,9024,7722,3184,9501,2982,7170,12762,4065,8924,3378,11079,2364,3995,10216,8523,3435,11677,2954,10779,10494,7657,9917,2922,9556,5174,8508,10243,3582,3011,11852,12732,4604,3857,5157,11555,10313,6560,4323,2204,4962,2473,8046,6482,12275,8927,7393,2574,5839,7745,3720,12623,4531,6139,12446,11032,5167,12350,12927,5968,7885,10197,4557,7518,10598,7410,11069,10258,4076,10165,12068,5862,2232,9252,3054,8842,5519,10639,7078,2621,2660,4059,10477,2382,3550,12300,9175,3418,12673,5122,12232,12100,11698,7735,3679,11545,3735,11751,12260,6820,2541,10990,7229,9031,3610,8910,4785,11212,2441,6652,9549,2705,4915,12437,2409,4466,12613,5734,12773,7042,5630,7989,3972,3867,8329,11766,4397,6032,7757,2277,6264,8756,10229,12664,4252,11865,5815,7834,9618,6990,5719,2969,4091,12608,7640,3134,5085,7692,10394,10548,8899,3814,2528,11191,7244,3514,3682,3286,6582,8746,10502,7576,4053,5341,2327,3799,7097,8683,10721,6646,10263,9113,8810,5826,4280,5391,8255,5702,3980,10330,11570,8832,8788,2628,8942,6427,2332,2826,6043,3297,3499,3065,9586,5177,3556,2872,5021,11980,8021,12461,7902,12881,11629,9626,4327,9391,12025,2200,5551,11452,6833,4402,11683,5113,4942,10035,12905,5658,3050,6267,2492,10907,11624,9885,12020,4461,4732,10543,12478,10473,11101,12709,11420,7767,8358,4316,11133,11056,9608,4636,12142,11089,4012,12372,10131,6075,12760,8354,8462,9814,12414,6748,12521,10848,11734,5053,3254,10748,6101,3413,12792,2801,7962,9016,4974,10986,8009,5615,11884,6955,9945,2359,6133,8604,12506,7389,3218,4048,8319,4525,4693,4845,8016,5428,8014,9624,9576,3963,10445,5978,10434,3119,11845,5373,3237,8572,12834,10760,8815,11304,5497,12033,5475,9772,4898,11536,12179,3622,6720,2196,4513,6395,11797,4676,6299,2460,2798,8544,3952,4951,8704,4301,8631,6175,11860,5075,6967,10830,7631,5915,9397,3407,2561,12325,12696,11869,5992,10528,10381,7318,8743,7998,2419,12639,12746,8177,5743,3441,10776,10620,5263,7604,4744,8132,11046,3032,6630,9100,10823,10195,8968,9288,12853,2349,7480,3723,10163,6541,7572,7976,12724,7313,6275,7523,10094,6724,9260,2450,3541,11052,10306,7913,3242,10919,9200,11742,2285,5317,11608,8673,3656,11828,9348,12632,10423,2519,4384,5149,8326,12429,9316,12164,5134,12532,11360,9893,2355,7738,2465,10158,12191,10285,4829,4934,4540,2566,4717,6908,5217,2766,2482,10629,6418,8090,9607,3333,10550,8307,11610,5603,12671,11093,12270,3920,2272,7333,2756,3162,7174,4223,2370,3215,8127,10651,2926,9684,4081,7687,5833,8049,2748,12442,11065,11769,5198,6869,6497,6409,5557,4184,12183,7020,2788,3834,10802,11216,11197,3225,5711,2546,2761,12282,8205,5402,7052,12736,8361,12891,9716,11787,10377,2963,12486,10635,6378,2402,11901,4448,6688,8262,12361,10090,5887,11539,6311,9139,5872,8626,9985,8708,7985,5679,10840,5722,2556,2585,8110,11148,7165,9049,10872,8164,5327,11110,9416,12168,8641,4685,11710,6203,9203,4874,5508,7742,8040,7155,10310,5855,5230,7706,12842,12265,11016,3262,10327,12704,3289,10321,5608,10274,8859,4269,4017,7910,9974,2894,2524,2376,8807,11805,8495,3547,10232,9062,2938,11566,3519,3945,10709,6898,4381,7472,3599,12028,4041,9418,10068,10425,3187,11983,3070,7938,4283,12914,12216,7497,6881,6510,6108,3240,2657,11615,7233,12170,11905,11703,4309,8470,2188,11411,10480,5962,8124,9719,10100,4032,8027,12862,5050,5099,12909,7704,11598,10461,3590,4590,3404,10127,12787,5752,10874,12011,6774,4946,12877,8872,3213,12473,5471,12716,7465,11841,5578,8064,3223,10044,5965,5185,11819,5546,3023,8534,9935,10611,9210,5567,4096,4837,4645,11060,10770,3651,8249,8665,5282,4218,2935,12524,10348,4413,3594,8300,9538,9776,12748,2753,12936,5207,5314,3487,5539,6636,12146,6123,2425,9290,12825,12280,10596,5784,11618,6372,9354,3302,8387,12278,4887,3355,10741,12867,11525,6261,9483,8244,12814,10140,9967,12547,7482,3532,6525,6048,6585,2361,5870,8408,4704,10448,4369,12227,8970,5381,6144,7529,10151,10532,12651,7643,11117,12668,9312,6920,2214,2422,7907,8135,9377,6147,3957,6217,6500,8237,2906,7379,6197,7607,8120,5303,8868,10898,3270,8693,2299,11355,9920,10037,8313,2669,5222,12656,2839,12537,2945,11338,9723,4213,4073,5093,5531,12136,10296,4374,8561,12894,6737,11531,11718,7307,2197,12369,9713,12464,4203,2812,9655,2267,10825,6847,10645,9042,6087,4430,8633,5920,12850,12114,10253,7113,3668,8156,6849,8661,3073,8103,11205,7566,2261,11188,12528,4264,7820,6974,7892,5599,9263,2446,11233,12111,7033,12755,7664,11964,7551,6414,3192,6678,3006,6080,8372,8998,5466,8782,10489,12727,10412,12000,6446,2553,5007,11761,2329,8413,11375,2911,4554,8198,5987,11310,12432,2835,6151,6504,9197,7366,4196,3539,11173,9610,6345,10660,4720,8440,5254,5775,4232,7030,9478,2725,11041,12534,12779,8719,10514,8821,11721,9249,5516,11245,5248,3806,11874,11113,3159,10893,5976,8541,12497,9106,2244,10108,4918,12765,3363,11605,12644,11781,9345,3178,3512,12224,8291,2999,5693,9740,3348,7916,2207,11507,5139,3908,6698,4209,4481,6785,6730,6476,10762,12060,4084,9001,7049,3490,5619,4741,4136,7526,9826,8116,8505,7773,12377,5358,5003,6641,12886,3881,5661,6768,5463,11161,4331,3009,10517,9097,10617,4426,4207,11316,4405,6320,4690,5528,9227,6672,7578,10632,12288,11062,4868,7650,6185,2994,2318,3395,12118,9069,10354,9430,11012,7298,2652,3293,8979,4735,12627,7539,6751,7897,4879,12239,3975,9639,9858,4566,2202,6517,12294,8106,7102,11579,2846,2564,3278,7013,11706,12701,10788,11391,6115,6664,10797,7475,3913,12174,2588,7554,11126,4593,10653,11230,2942,4255,11738,5716,8592,12918,7087,12684,8003,2715,7942,6472,11909,3507,5294,10540,3842,11857,5125,7211,4937,6934,11562,6885,4939,5478,5399,4366,3082,12313,11808,10856,5944,4534,3659,8701,4200,12858,5980,10667,11726,3228,11594,4641,11855,8096,2407,4894,8350,8364,11252,2850,11988,5790,6384,4314,12187,9991,2688,6421,11295,5555,3026,3127,11661,3080,11428,5955,10915,8612,5431,8498,7264,9634,3305,11974,12364,3063,9599,2700,8428,7105,3554,12514,10717,7667,8216,7662,12419,9809,7947,3823,8917,5560,2337,6125,5154,3828,8391,8840,11180,9413,2903,11637,3359,7127,9963,6330,3853,6206,9435,10509,3769,2468,12871,5277,12512,12630,12262,8061,8850,7612,2728,10432,8087,3366,12039,2675,2247,5147,10129,7752,12328,2500,10536,12439,4959,7515,8547,7919,2379,4624,9151,4611,11830,7461,4436,2543,11054,11882,10160,2279,7585,8602,7163,5809,9242,9632,11005,12856,8043,2807,3156,11879,6105,6531,12829,10451,6622,6220,4392,11369,10714,4278,5917,2696,2347,4780,5308,8153,2792,8681,10214,6284,3168,2435,3284,6928,7363,7099,3400,3139,10754,10241,9395,2458,8946,12343,4424,4138,12933,12912,2479,11150,5749,4325,9912,4587,10364,10767,10806,4770,10464,9665,7764,11978,10526,6970,3171,2960,6068,4944,10821,12883,6861,4656,11450,7816,10199,11681,12484,12495,2209,2743,11541,10905,12722,2226,5860,5389,8098,8579,6814,3665,6711,12452,12302,11076,2594,6639,8584,3336,11433,7700,4834,10077,3465,5055,6903,10072,5724,6818,7653,3789,3709,3825,7359,12775,4666,11832,5191,11039,5351,7996,12516,2823,7167,8854,10325,9343,11867,5813,6770,10428,5228,8722,6494,3003,5394,3331,12113,5104,3368,12387,12050,3662,2416,11091,11145,4261,11918,7327,4182,4293,5287,10937,8172,11497,9856,3181,2384,8488,2786,12181,9470,4321,2399,6484,12273,8837,8501,6118,7715,12323,8638,3267,4774,8304,11658,11815,11552,11366,4387,11405,6412,11454,3529,3677,7157,9955,11227,12448,3793,12675,2680,12152,10087,5144,9799,8953,9660,7520,7574,5672,11772,5128,4098,4570,11894,5196,4372,9162,3761,9643,4306,5194,12480,11700,12298,5336,12125,4619,9427,9321,5864,10909,9239,8324,10733,11140,10041,3987,12285,4663,4597,9976,6782,3992,11744,12391,9812,4039,11131,10838,7081,7542,2517,12108,4014,4399,12658,3860,3785,7634,9806,10291,11960,4378,3232,5971,12162,6693,9229,3291,8478,6822,5796,4356,10173,3601,12374,8296,11589,10601,3892,10443,2522,3373,7489,7712,9523,11219,5078,4843,3521,11843,2736,12292,7121,12681,11341,6906,11612,3690,6226,8621,3164,10804,4474,11759,7323,10649,7727,4029,6627,9466,4777,4051,11214,11199,8521,11557,6294,2334,4286,11194,10168,10379,8510,4968,6735,11627,12734,3479,9959,5564,8395,9874,9299,6287,12801,6765,9752,11209,11067,2404,6889,11326,3426,12729,5378,11668,9795,8268,2223,6682,11776,5642,6398,11422,4193,9293,12022,7291,12466,3045,3673,6309,5110,12444,9382,2783,10781,10224,12102,6269,2549,10092,7925,11236,2810,5151,2583,4019,12007,2502,2241,7214,4848,2966,12435,2430,6099,7987,7227,11621,2600,12220,7506,11050,11958,5637,10988,6993,10255,11358,9474,5581,6209,4876,9504,8093,9583,5280,9737,3817,3965,8730,3020,9193,7708,2507,7370,5958,3392,7025,10308,4229,10845,6595,7755,11425,4659,4713,7617,8453,10323,4395,10642,5891,9979,2864,9066,3076,3113,6548,7176,2484,5645,7252,4088,7246,4363,8857,2372,11430,12144,5344,3341,11298,5877,10118,2866,6857,11754,4977,2191,11990,3960,9568,3474,10383,8786,6297,2672,2879,3950,12149,3437,6961,4520,4891,10934,10245,4723,10344,4949,4767,9784,2690,11631,11985,6984,5436,10900,7861,11241,10902,12488,2297,2438,2238,9748,11048,4056,6686,3052,3637,10745,5664,2351,8380,12070,9254,6739,7295,8818,10750,8405,6948,11648,11896,5911,2980,3035,12316,6896,12047,10096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP024+2 : TPTP v8.1.2. Released v3.4.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 20:17:24 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.85/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.47/1.18 % [INFO] Parsing done (382ms).
% 2.47/1.19 % [INFO] Running in sequential loop mode.
% 2.94/1.38 % [INFO] eprover registered as external prover.
% 2.94/1.38 % [INFO] cvc4 registered as external prover.
% 2.94/1.38 % [INFO] Scanning for conjecture ...
% 3.65/1.59 % [INFO] Found a conjecture and 3582 axioms. Running axiom selection ...
% 5.28/2.14 % [INFO] Axiom selection finished. Selected 2175 axioms (removed 1407 axioms).
% 7.74/3.02 % [INFO] Problem is first-order (TPTP FOF).
% 7.96/3.07 % [INFO] Type checking passed.
% 7.96/3.07 % [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 ...
% 129.91/33.39 % External prover 'cvc4' found a proof!
% 129.91/33.39 % [INFO] Killing All external provers ...
% 129.91/33.39 % Time passed: 32864ms (effective reasoning time: 32202ms)
% 129.91/33.40 % 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)>
% 129.91/33.40 % Axioms used in derivation (2175): t4_tsep_1, t119_funct_2, cc31_tex_2, t76_tex_4, fc3_tex_2, t39_relset_1, t108_tops_1, t49_tops_3, t32_funcop_1, fc1_t_0topsp, fc1_tops_1, t5_boole, fc8_tops_1, t12_tex_2, t9_connsp_2, t29_tsep_1, t70_tex_2, t72_xboole_1, t86_partfun1, cc17_tex_3, t62_partfun1, t23_funct_2, t158_relat_1, d4_tex_4, t34_subset_1, t45_eqrel_1, t51_partfun1, redefinition_m2_relset_1, t48_tex_3, t13_zfmisc_1, t30_funct_2, t55_funcop_1, d4_tex_3, t13_relset_1, t11_tsp_1, cc1_tops_1, t181_relat_1, t32_tsep_1, cc24_tex_2, t52_tex_2, t131_partfun1, t38_funcop_1, t175_relat_1, t20_tex_2, t14_tsp_1, t72_tops_2, d1_tsp_1, dt_k2_borsuk_1, t48_funcop_1, t9_tex_3, t44_tops_2, t70_tops_1, t12_borsuk_1, t60_tex_2, t62_borsuk_1, t147_funct_1, t84_tops_1, redefinition_k4_pre_topc, t8_tex_4, dt_k2_tex_4, t51_tex_2, t18_tex_2, t19_xboole_1, t80_tex_4, t19_pcomps_1, t67_tops_1, t42_tops_2, t17_xboole_1, t112_xboole_1, t39_tex_4, t130_partfun1, t18_tsep_1, t42_subset_1, t43_subset_1, rc18_tex_2, t66_tsep_1, t42_relat_2, fc1_zfmisc_1, t27_pcomps_1, t76_tops_1, t54_relat_1, t6_tex_4, t35_subset_1, d1_tarski, t26_tops_3, t16_tsep_1, t135_zfmisc_1, t17_zfmisc_1, t53_tex_2, t54_tops_1, t148_funct_1, t25_relset_1, d20_binop_1, fc12_tops_1, d6_t_0topsp, t66_funct_2, t143_funct_1, d6_tex_2, dt_m2_connsp_2, t19_eqrel_1, t67_relat_1, t66_partfun1, t45_pre_topc, t154_relat_1, d4_funct_1, t30_tops_3, t60_funcop_1, t70_funct_2, dt_k3_borsuk_1, t38_tex_3, cc2_tex_2, t7_tops_3, t38_tsep_1, cc44_tex_2, t53_subset_1, t8_pcomps_1, t35_tops_1, d1_tex_3, t41_pre_topc, idempotence_k3_xboole_0, t110_xboole_1, t63_funcop_1, t91_tex_4, redefinition_k5_subset_1, t46_tex_4, t73_xboole_1, t37_borsuk_1, d14_binop_1, t79_tops_1, t12_tops_3, dt_k5_relset_1, d5_relat_1, cc8_tsp_1, t105_zfmisc_1, t62_tops_3, t97_tops_1, dt_k19_borsuk_1, t65_tex_3, t15_tsep_1, cc3_tex_4, t77_partfun1, t67_funcop_1, d10_binop_1, t57_funcop_1, t47_relset_1, t161_funct_2, t1_boole, cc14_tex_3, t62_relat_1, t7_subset_1, t92_xboole_1, t8_t_0topsp, t11_tex_4, d3_connsp_2, t66_xboole_1, t23_xboole_1, fraenkel_a_2_1_borsuk_1, t67_tex_4, t64_tex_4, cc40_tex_2, fc2_pre_topc, t27_funct_2, d14_tex_4, t50_relat_1, t23_connsp_2, t91_tops_1, dt_k2_tops_1, t23_tex_2, t33_tops_2, t20_funct_2, redefinition_m2_tsp_1, t28_tex_3, dt_k8_funcop_1, cc2_tsp_1, irreflexivity_r1_subset_1, d12_borsuk_1, t69_tex_2, d5_membered, dt_k5_tex_4, t3_xboole_1, fraenkel_a_2_8_tex_4, t35_tsep_1, t137_funct_1, d3_subset_1, t7_connsp_2, t183_relat_1, d2_tops_3, t25_tsep_1, dt_k4_relset_1, t87_tops_1, rc20_tex_2, t156_funct_1, t59_partfun1, t1_subset, t45_funcop_1, fc1_xboole_0, t10_tops_2, t45_tex_4, t5_borsuk_1, t13_tex_2, t25_funct_1, t113_zfmisc_1, t140_partfun1, fc43_membered, t16_funct_2, t19_tex_3, t51_borsuk_1, rc12_tex_2, t17_tops_2, t116_partfun1, dt_k20_borsuk_1, dt_k7_subset_1, t28_tops_2, t113_xboole_1, t111_zfmisc_1, dt_k2_subset_1, rc4_pre_topc, d13_borsuk_1, t47_tops_2, d2_tsp_2, t81_partfun1, t58_tex_4, t56_partfun1, t8_subset_1, t81_tops_3, t16_tsp_1, d1_pcomps_1, t53_funct_2, t29_borsuk_1, d5_tarski, t25_tops_3, rc1_borsuk_1, t50_borsuk_1, t15_funct_1, rc3_tops_1, fc6_tex_4, fc4_relat_1, t79_tops_3, t28_tops_3, t4_ordinal1, t4_tex_3, t35_borsuk_1, s12_funct_2, t23_tops_2, t53_funcop_1, t158_funct_1, redefinition_k10_borsuk_1, t44_relat_1, dt_k4_pcomps_1, s3_funct_2, t12_tsp_1, redefinition_k7_funct_2, t43_tex_3, t147_relat_1, t10_partfun1, fc34_membered, d2_connsp_2, t22_funct_1, t2_tex_4, t11_t_0topsp, t96_zfmisc_1, t42_zfmisc_1, t6_xboole_1, dt_k7_tex_4, t158_partfun1, t28_tex_2, t33_tex_2, d5_xboole_0, t12_tex_3, dt_k7_relset_1, t90_tops_1, t29_subset_1, dt_k8_borsuk_1, dt_k2_tsep_1, t151_funct_1, cc9_tex_2, t77_tex_4, t52_zfmisc_1, t144_relat_1, t8_tex_3, t71_tex_4, t10_connsp_2, t44_eqrel_1, cc8_tex_4, fc4_subset_1, dt_k4_t_0topsp, t10_tex_4, dt_k1_tops_1, d5_tsp_2, fc31_membered, t21_tex_2, t34_relat_2, t52_tops_2, t9_borsuk_1, t79_funcop_1, fc1_numbers, d7_tex_2, dt_k3_funct_2, t74_funct_2, t168_funct_2, t36_tops_2, dt_k4_tsp_2, t54_partfun1, t81_zfmisc_1, t97_tsep_1, t7_tex_4, rc1_membered, t7_funct_2, t50_tops_3, fraenkel_a_2_3_tex_4, t10_relset_1, t43_relat_2, t135_partfun1, t146_funct_2, fc4_tops_1, fraenkel_a_3_0_borsuk_1, t18_xboole_1, t4_funcop_1, cc37_tex_2, t46_tops_2, t14_binop_1, t74_tex_4, dt_k1_subset_1, t117_partfun1, t13_funcop_1, redefinition_k4_tsp_2, t19_zfmisc_1, t3_connsp_2, d8_funct_1, t19_relat_1, t70_xboole_1, t28_binop_1, t74_tsep_1, dt_g2_struct_0, t6_tsep_1, d8_tex_4, t35_zfmisc_1, t88_tops_1, cc23_tex_3, fc11_tops_1, d6_pre_topc, t166_funct_2, t65_tsep_1, t67_borsuk_1, fc11_tex_4, t9_tsep_1, t47_relat_1, t5_t_0topsp, fc9_relat_1, t148_partfun1, abstractness_v2_struct_0, t68_xboole_1, t21_membered, d7_binop_1, d16_tex_4, t7_t_0topsp, t25_xboole_1, existence_m1_struct_0, t45_tops_3, t55_tops_3, t2_boole, t69_tops_1, t28_funcop_1, t23_tops_3, t106_tops_1, rc2_struct_0, cc43_tex_2, t102_tops_1, t26_tex_4, t31_tex_2, t1_funcop_1, fc7_tex_4, t117_zfmisc_1, t65_partfun1, t186_partfun1, t44_funct_2, cc1_tex_3, d10_borsuk_1, t24_tex_2, rc7_tex_3, t117_funct_1, t61_tops_1, cc20_tex_3, dt_k4_subset_1, t132_partfun1, rc6_tex_3, fc6_tops_1, t27_xboole_1, t59_tops_1, t71_xboole_1, rc12_tex_3, t122_zfmisc_1, d13_pre_topc, t36_tex_3, t50_pre_topc, dt_k1_struct_0, redefinition_k1_pcomps_1, dt_k16_borsuk_1, t34_tex_3, t12_pre_topc, d11_borsuk_1, t73_funcop_1, t23_tsep_1, dt_m2_tsp_1, t23_pre_topc, fc6_funcop_1, t82_tops_1, dt_m1_borsuk_1, t25_pre_topc, cc5_tops_1, t73_tex_3, t110_zfmisc_1, t15_tops_3, t47_tops_3, fc17_tex_4, t43_zfmisc_1, dt_u2_struct_0, t29_numbers, t56_tops_1, t99_zfmisc_1, rc2_partfun1, t18_relat_1, cc1_tsp_1, t171_relat_1, t45_zfmisc_1, t50_funct_2, d1_tsep_1, d6_pcomps_1, symmetry_r2_tsep_1, t61_tex_2, t103_zfmisc_1, t63_partfun1, t153_funct_1, t95_zfmisc_1, t96_partfun1, t78_funcop_1, t15_relset_1, t49_tex_2, t77_tops_1, t73_tops_1, t56_tsep_1, t61_subset_1, d1_tops_2, rc3_funct_1, fc5_tops_1, t13_pre_topc, t29_tex_2, t32_tops_2, t16_t_0topsp, t49_funct_2, symmetry_r4_tsep_1, t17_membered, fc1_funct_1, t27_tex_3, t29_relat_2, t57_tsep_1, t68_borsuk_1, t162_partfun1, t49_tex_3, t64_funcop_1, t40_eqrel_1, t99_tsep_1, t30_relat_2, dt_k6_partfun1, fc1_pre_topc, t29_tops_2, d3_tex_4, cc33_tex_2, t32_tops_1, t39_relat_1, cc18_tex_3, dt_k3_metric_1, t78_borsuk_1, t56_relat_1, t26_funct_2, cc1_relat_1, t30_membered, t70_tsep_1, t29_partfun1, t70_partfun1, t71_tops_1, cc16_tex_2, t66_tex_3, d1_struct_0, t8_tsp_1, dt_k9_borsuk_1, t27_zfmisc_1, fc21_tex_4, d6_connsp_2, t17_funct_1, d6_tops_1, t9_xboole_1, t37_pcomps_1, fc3_borsuk_1, dt_k1_connsp_2, t59_subset_1, t41_zfmisc_1, t11_connsp_2, cc3_tops_1, dt_m2_relset_1, t10_borsuk_1, rc3_pre_topc, dt_k7_funct_2, t6_eqrel_1, t131_zfmisc_1, t13_tops_3, redefinition_k2_funct_2, t95_xboole_1, t68_tex_2, idempotence_k5_subset_1, t50_zfmisc_1, d7_partfun1, t46_borsuk_1, t2_funct_1, t36_subset_1, symmetry_r3_tsep_1, t74_tops_2, t49_zfmisc_1, t21_tsp_1, dt_k1_pre_topc, t38_tops_3, t56_borsuk_1, t81_tsep_1, t3_tsep_1, d7_connsp_2, commutativity_k3_xboole_0, t27_tops_3, t176_partfun1, t12_binop_1, t62_funct_2, t3_funcop_1, fc28_membered, t51_tops_3, t130_funct_2, t53_tsep_1, t4_connsp_2, t24_funct_2, t83_funcop_1, t34_tsep_1, t32_subset_1, t115_zfmisc_1, t52_funcop_1, t80_tops_1, t76_funct_2, t46_pre_topc, t152_funct_2, d3_pre_topc, t35_tex_2, t48_tops_3, t80_funcop_1, t65_funct_2, t19_funct_1, fc32_membered, fc30_membered, t104_tops_1, fc42_membered, t12_t_0topsp, t5_tex_2, s13_funct_2, t21_connsp_2, t50_tops_1, d2_tarski, dt_k2_binop_1, t137_zfmisc_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, t34_tops_1, t75_tex_2, t2_partfun1, rc3_tsp_1, t20_tsp_1, t35_tops_2, t30_tex_4, fc5_pre_topc, involutiveness_k3_subset_1, t13_relat_1, d2_tops_2, rc1_funct_1, t17_binop_1, t51_tex_3, t25_funct_2, fc2_xboole_0, t87_partfun1, t21_tops_3, t60_tops_3, d14_tsp_1, fraenkel_a_2_5_tex_4, t15_binop_1, rc4_tex_3, rc4_tsp_1, t168_relat_1, d6_binop_1, t22_funcop_1, rc6_pre_topc, t64_funct_2, d3_t_0topsp, d1_tops_3, t111_tops_1, t31_tops_3, t76_partfun1, cc11_tex_3, t34_partfun1, dt_k9_funct_2, t43_tops_1, t32_connsp_2, t42_tex_4, t27_tex_2, t46_funct_2, t72_tex_3, t175_partfun1, cc29_tex_2, t48_funct_2, t173_relat_1, cc25_tex_2, t154_funct_2, t19_tsep_1, t66_tops_1, t48_tex_2, t16_tex_4, t172_relat_1, t27_relat_1, t53_tex_3, t156_funct_2, fc24_membered, t85_tex_4, t67_tsep_1, d1_xboole_0, dt_m1_eqrel_1, t49_funct_1, t65_tops_1, dt_k21_borsuk_1, cc7_tex_2, t108_xboole_1, t77_tex_2, t37_tops_3, t20_tex_3, redefinition_k8_funcop_1, t22_tsep_1, t38_tex_4, fc25_membered, t17_tex_2, t40_tex_3, d2_tex_2, t52_pre_topc, t64_relat_1, t138_zfmisc_1, t25_subset_1, rc1_tops_1, fraenkel_a_2_0_borsuk_1, d2_funcop_1, d14_borsuk_1, cc2_tex_4, rc10_tex_2, t23_funct_1, t73_tops_3, t130_zfmisc_1, t33_tex_4, t60_tex_3, dt_k10_funcop_1, rc17_tex_2, cc1_tex_2, t108_zfmisc_1, fraenkel_a_1_0_t_0topsp, t165_funct_2, rc5_tex_3, cc10_tex_2, t75_funct_2, t29_funct_2, t60_partfun1, t118_funct_2, t14_relset_1, dt_k11_borsuk_1, t16_relset_1, t46_tex_3, t56_zfmisc_1, t9_tsp_1, existence_m2_connsp_2, t27_relset_1, t64_borsuk_1, d21_borsuk_1, redefinition_k19_borsuk_1, t15_funcop_1, dt_l1_pre_topc, t52_relset_1, t118_zfmisc_1, t55_partfun1, t91_tsep_1, s4_subset_1, t8_funct_2, t3_tops_2, fc3_pcomps_1, t57_tex_4, t78_tops_3, t55_tops_2, t77_borsuk_1, t61_tops_3, t36_pcomps_1, t43_tex_4, t53_relset_1, t49_borsuk_1, fc2_borsuk_1, d13_relat_1, t46_zfmisc_1, t53_tops_3, t33_eqrel_1, t31_partfun1, t92_tsep_1, t13_t_0topsp, t171_partfun1, t164_funct_2, fc2_funct_2, t6_boole, t12_funct_1, t18_tex_3, t3_funct_2, t18_subset_1, dt_k3_tsp_2, rc2_subset_1, t19_tex_2, t26_borsuk_1, t9_tops_3, t67_tops_2, t30_borsuk_1, t74_borsuk_1, dt_k6_subset_1, t43_pre_topc, t47_funct_2, t15_pcomps_1, d3_tops_2, t80_borsuk_1, t35_tops_3, t13_tsep_1, d1_relat_1, t34_tops_3, t101_tops_1, fc12_tex_4, t185_partfun1, t42_tops_3, t1_xboole_1, t26_relset_1, t86_tops_1, rc1_tex_4, t41_tops_1, t160_funct_1, fraenkel_a_2_9_tex_4, t65_tex_2, t17_pcomps_1, commutativity_k2_xboole_0, t5_subset, t40_tops_2, t25_tops_2, t64_partfun1, t52_relat_1, t35_funcop_1, t18_pcomps_1, t77_funct_2, free_g1_pre_topc, t4_tsp_1, cc19_tex_2, rc5_tsp_1, t73_tex_4, t20_funct_1, t4_tex_2, cc8_tex_3, t16_pre_topc, t54_borsuk_1, existence_l2_struct_0, rc5_tops_1, t55_relat_1, cc9_tex_3, t30_tsep_1, t68_partfun1, t10_tops_3, fraenkel_a_2_0_tex_4, t3_partfun1, t32_partfun1, t67_tex_2, t83_partfun1, redefinition_k4_funct_2, d6_tarski, t4_relat_1, commutativity_k1_tsep_1, t28_subset_1, fc5_funcop_1, t22_tops_1, fc33_membered, cc15_tex_3, t75_xboole_1, t13_eqrel_1, fc16_membered, t79_partfun1, fc3_subset_1, t128_zfmisc_1, t76_tsep_1, t149_funct_1, t2_tex_3, cc19_membered, t65_xboole_1, d5_tops_1, cc4_tex_3, fraenkel_a_3_1_borsuk_1, t25_zfmisc_1, d4_relat_1, t53_borsuk_1, t94_zfmisc_1, t13_tex_4, t24_borsuk_1, t46_tops_1, t4_xboole_0, t62_tex_2, t41_funcop_1, t8_tops_1, t20_tops_3, t48_zfmisc_1, d12_tsp_1, t17_tsp_1, t95_tsep_1, d8_tsp_1, t27_tops_1, fc19_tex_4, d6_partfun1, t150_relat_1, existence_m1_relset_1, commutativity_k5_subset_1, t54_tex_2, t79_borsuk_1, t1_zfmisc_1, cc6_tex_4, fc2_tops_1, t44_tex_3, fc21_membered, t163_relat_1, t18_pre_topc, t36_tsep_1, d4_pcomps_1, dt_k1_tops_2, t41_tops_3, dt_k1_tex_2, redefinition_k14_borsuk_1, t84_borsuk_1, t64_tops_1, t110_tops_1, t123_zfmisc_1, fc2_subset_1, t2_membered, t40_tex_2, t31_eqrel_1, t45_funct_2, t42_tex_3, t41_tex_4, cc47_tex_2, cc30_tex_3, t79_zfmisc_1, rc7_tsp_1, t5_funct_2, t176_relat_1, dt_k8_funct_2, t63_tex_3, t86_tex_4, t15_tsp_1, t34_tops_2, t68_tops_3, fc11_membered, rc19_tex_2, t62_tops_1, t97_zfmisc_1, d11_tex_4, t40_funct_2, t2_tops_1, dt_k7_borsuk_1, t20_connsp_2, t37_tex_4, t75_tops_1, t167_funct_2, dt_k18_borsuk_1, cc22_tex_3, t54_tops_2, t53_partfun1, rc6_tex_2, t16_tops_3, cc15_tex_2, t79_tex_4, t60_zfmisc_1, t19_tops_3, t83_tops_3, t89_tex_4, cc7_tsp_1, dt_m1_struct_0, t11_funct_2, fc10_tops_1, t28_partfun1, t76_tex_2, t57_tops_1, cc18_tex_2, t44_pre_topc, t102_zfmisc_1, t3_tex_3, t10_tex_3, t14_tex_4, t12_tex_4, t27_funcop_1, d19_tex_4, t84_tops_3, t71_tex_3, t72_partfun1, t8_funct_1, t51_funcop_1, t121_funct_1, t75_borsuk_1, t6_tops_3, t8_tex_2, fc4_eqrel_1, t45_tops_2, t9_relat_1, fc6_membered, t32_tex_2, t2_tarski, t16_funct_1, t28_zfmisc_1, t14_relat_1, d1_tex_4, t142_funct_2, t82_funct_2, t24_tex_3, rc4_tops_1, t62_subset_1, t122_funct_1, t14_tops_3, t25_borsuk_1, dt_k15_borsuk_1, t166_relat_1, redefinition_k8_eqrel_1, t2_zfmisc_1, d17_tex_4, d4_tsp_1, dt_k1_borsuk_1, d11_tsp_1, t63_tsep_1, t61_funcop_1, t114_xboole_1, t8_zfmisc_1, t29_eqrel_1, t14_pcomps_1, t74_funcop_1, t7_tex_3, dt_k1_partfun1, t11_tops_2, t52_subset_1, t5_ordinal1, t16_funcop_1, t169_funct_2, d2_xboole_0, t1_tsp_2, t30_xboole_1, fc4_tex_4, cc49_tex_2, rc11_tex_3, t98_tsep_1, d9_tsp_1, t32_tops_3, t146_funct_1, t30_tex_3, t5_tops_3, t47_borsuk_1, d2_funct_2, cc2_eqrel_1, redefinition_v3_tsp_1, d2_pre_topc, d13_funct_1, t50_tex_4, t133_funct_2, t10_t_0topsp, t73_tsep_1, t57_zfmisc_1, t125_funct_1, t52_tex_3, t21_xboole_1, t98_zfmisc_1, t114_partfun1, t58_subset_1, dt_k11_relset_1, t9_pcomps_1, dt_k4_relat_1, rc5_tex_2, t45_tex_2, d5_pre_topc, t4_subset, cc11_tsp_1, fc26_membered, t76_xboole_1, t71_tops_2, cc38_tex_2, t25_funcop_1, dt_k7_eqrel_1, fc3_xboole_0, t178_relat_1, t38_subset_1, t53_pre_topc, dt_k4_pre_topc, t81_tops_1, cc6_tsp_1, t39_tops_1, cc1_funct_2, t96_tsep_1, t78_tsep_1, t39_subset_1, cc31_tex_3, t14_funct_1, cc1_partfun1, dt_k22_borsuk_1, d4_tarski, t13_tops_2, fc2_pcomps_1, t33_tsep_1, t27_connsp_2, abstractness_v1_pre_topc, t20_tex_4, t147_partfun1, d8_tsep_1, t47_funcop_1, t22_relat_2, t132_funct_2, t65_funcop_1, t61_partfun1, t61_tsep_1, d12_tex_4, t83_tsep_1, fraenkel_a_3_1_pcomps_1, t47_tex_3, t10_membered, t36_tex_2, t9_zfmisc_1, t148_funct_2, t30_tops_1, t14_connsp_2, t67_xboole_1, d12_binop_1, t51_funct_2, d8_pre_topc, d10_tex_4, t12_zfmisc_1, t87_tex_4, t174_relat_1, d7_borsuk_1, t15_tex_2, t41_borsuk_1, t12_tops_2, t56_subset_1, redefinition_k10_relset_1, dt_k5_borsuk_1, d3_borsuk_1, t25_membered, rc16_tex_2, t49_tops_1, t58_zfmisc_1, t20_borsuk_1, t17_funct_2, dt_k5_pcomps_1, t58_tops_1, rc15_tex_2, t93_partfun1, t1_xboole_0, t44_tops_3, involutiveness_k4_relat_1, d4_partfun1, t29_xboole_1, d5_connsp_2, t25_tex_4, dt_k17_borsuk_1, t179_relat_1, t52_tops_1, t39_tsep_1, t72_borsuk_1, t63_tops_1, dt_k3_pcomps_1, t6_t_0topsp, t9_t_0topsp, d5_tex_2, rc2_tex_4, t7_tsep_1, t72_tsep_1, d10_pre_topc, commutativity_k5_xboole_0, cc6_tops_1, cc20_membered, t7_boole, fraenkel_a_2_3_borsuk_1, redefinition_k2_tsp_2, t53_tex_4, t7_tsp_1, t105_tops_1, t139_zfmisc_1, d8_pcomps_1, t18_tex_4, d5_tops_2, t74_tops_3, cc13_tex_3, rc6_tsp_1, t160_funct_2, cc1_funct_1, t25_tex_2, t37_tops_1, t31_tex_4, t4_funct_2, t24_funcop_1, t27_membered, redefinition_k5_borsuk_1, t27_pre_topc, t14_tsep_1, t60_tex_4, t136_partfun1, t24_connsp_2, fc9_tops_1, t58_tex_2, fc45_membered, t66_tex_4, fc4_pre_topc, s11_funct_2, t31_tops_2, t11_binop_1, t104_zfmisc_1, symmetry_r1_subset_1, t138_partfun1, dt_g1_pre_topc, t61_borsuk_1, dt_k10_borsuk_1, rc3_struct_0, t30_tex_2, t55_zfmisc_1, cc35_tex_2, t20_tops_2, t103_tops_1, cc28_tex_3, t143_relat_1, t1_t_0topsp, d2_subset_1, t55_tex_2, free_g1_metric_1, t3_t_0topsp, fc1_subset_1, cc4_tex_4, d4_tops_3, t33_zfmisc_1, t58_tops_3, fraenkel_a_2_1_tex_4, t5_tex_3, commutativity_k2_struct_0, fc29_membered, t22_relat_1, rc3_tex_2, rc1_t_0topsp, dt_k6_borsuk_1, t157_funct_1, t16_pcomps_1, t85_partfun1, t3_ordinal1, t82_tops_3, t75_tex_3, d5_eqrel_1, rc10_tex_3, t92_tops_1, t149_funct_2, t21_funct_2, d5_t_0topsp, d7_tops_1, fc2_membered, cc21_tex_3, t15_tex_3, t23_borsuk_1, t11_tops_3, t22_tops_2, rc14_tex_2, t66_funcop_1, t21_tops_2, fraenkel_a_2_7_tex_4, t31_relat_2, t16_subset_1, dt_k2_partfun1, t20_eqrel_1, fc10_tex_4, t59_borsuk_1, t26_zfmisc_1, t62_tsep_1, t69_partfun1, t7_ordinal1, t38_relset_1, t153_relat_1, rc2_funct_1, t49_partfun1, d8_tex_2, t9_funct_2, t160_relat_1, t54_tex_4, fc10_relat_1, rc1_subset_1, t81_funcop_1, dt_k2_tsp_2, t72_tex_4, t158_funct_2, t61_tex_3, cc4_membered, t48_funct_1, t152_funct_1, dt_k3_tex_4, t16_tex_3, rc11_tex_2, t49_relset_1, rc5_borsuk_1, cc26_tex_2, t47_funct_1, t28_borsuk_1, t22_tex_3, dt_m1_pre_topc, t31_xboole_1, t63_zfmisc_1, dt_k6_funcop_1, t4_subset_1, t19_funct_2, t51_funct_1, t13_borsuk_1, cc14_tex_2, cc16_tex_3, t162_funct_2, t90_tsep_1, t41_tops_2, t4_tops_3, t22_pcomps_1, t8_connsp_2, t14_zfmisc_1, rc1_funct_2, t24_xboole_1, t80_tsep_1, d2_tops_1, t46_tex_2, t31_connsp_2, t90_tex_4, t68_tex_3, t151_relat_1, t87_tsep_1, d3_tops_3, d3_tsp_2, t20_xboole_1, d14_relat_1, t124_zfmisc_1, t113_funct_2, t71_partfun1, t14_eqrel_1, t69_xboole_1, d5_funct_2, t159_funct_2, t116_zfmisc_1, cc18_membered, d7_xboole_0, t49_tsep_1, fc5_relat_1, redefinition_r1_subset_1, cc2_tex_3, t76_funcop_1, dt_k6_tex_4, t39_tex_2, t4_borsuk_1, t67_tops_3, t45_relat_1, d1_tex_2, fc1_tex_4, cc29_tex_3, dt_k2_struct_0, t14_funct_2, t155_funct_2, t41_tsep_1, s2_subset_1, t66_tops_2, t47_pre_topc, t6_tex_2, cc22_tex_2, t70_borsuk_1, t86_tsep_1, fc5_borsuk_1, rc8_tex_3, t95_tops_1, t16_zfmisc_1, t24_pcomps_1, t63_tex_2, t101_zfmisc_1, t56_tex_2, rc13_tex_3, t37_tex_3, d6_tex_4, t3_tops_3, t17_borsuk_1, t2_t_0topsp, cc19_tex_3, t8_tsep_1, fc1_borsuk_1, cc11_tex_2, dt_k1_tex_4, t33_connsp_2, existence_m2_tsp_1, t78_tex_4, t48_tex_4, t57_tex_3, t55_tops_1, t60_funct_2, t62_tex_3, fraenkel_a_2_2_borsuk_1, t32_zfmisc_1, t85_tsep_1, d5_tsep_1, existence_m1_pre_topc, t77_tops_3, s4_funct_2, t23_pcomps_1, cc2_funct_1, t85_borsuk_1, t120_zfmisc_1, t76_borsuk_1, t28_eqrel_1, t21_funcop_1, t93_tops_1, cc3_tex_2, t169_partfun1, dt_k3_t_0topsp, t18_funct_1, cc9_membered, t21_tsep_1, t38_borsuk_1, t40_tops_3, t30_eqrel_1, t4_relset_1, t94_tsep_1, dt_k4_funct_2, t31_subset_1, t3_subset, cc1_relset_1, d8_borsuk_1, cc1_eqrel_1, t22_relset_1, d2_binop_1, s1_subset_1, cc10_tex_3, redefinition_k3_tsp_2, t52_borsuk_1, t59_tex_3, t29_tex_4, t55_subset_1, t79_funct_2, t46_funct_1, t64_tex_2, t39_tops_3, cc27_tex_3, t48_tsep_1, t56_funcop_1, t136_funct_2, t6_borsuk_1, t30_connsp_2, redefinition_k21_borsuk_1, commutativity_k7_subset_1, t23_tex_4, d2_zfmisc_1, fc11_relat_1, cc5_tex_3, existence_m1_subset_1, t17_tex_3, commutativity_k2_tarski, t3_relat_1, t36_borsuk_1, d7_relat_1, d4_eqrel_1, t24_relat_1, cc7_tex_3, t8_relset_1, t44_tex_2, t44_zfmisc_1, t42_tex_2, rc1_tex_3, existence_m2_subset_1, t106_zfmisc_1, t51_tops_2, t51_tex_4, cc4_tsp_1, t71_tops_3, t64_tsep_1, cc15_membered, t63_borsuk_1, t73_funct_2, t30_subset_1, t42_borsuk_1, d17_binop_1, t81_tex_4, dt_k2_funct_2, t14_tex_3, t32_tex_3, t12_connsp_2, t84_funcop_1, redefinition_k4_subset_1, t54_tsep_1, rc4_tex_2, t64_tops_2, t14_xboole_1, t11_relset_1, d2_tex_4, d8_relat_1, fc20_tex_4, t63_tops_2, t60_tsep_1, t35_tex_3, t134_funct_2, t19_numbers, t145_funct_1, t13_tex_3, t5_pre_topc, t15_subset_1, t18_tsp_1, t75_tsep_1, free_g2_struct_0, t37_funct_2, t17_relset_1, t54_tops_3, dt_k2_t_0topsp, t31_funcop_1, t118_funct_1, t132_zfmisc_1, existence_m1_tsp_1, t38_tops_1, d9_binop_1, t27_tops_2, t18_borsuk_1, existence_m1_connsp_2, t72_tops_1, t29_zfmisc_1, t92_zfmisc_1, t146_relat_1, t57_tops_2, t99_partfun1, t107_zfmisc_1, t13_pcomps_1, dt_k12_borsuk_1, t24_tops_2, rc2_tsep_1, t22_tex_4, t49_funcop_1, t56_tex_3, t49_tops_2, t54_pre_topc, dt_k24_borsuk_1, t142_partfun1, t121_funct_2, cc6_tex_3, t71_tex_2, t114_zfmisc_1, cc5_tex_2, fc44_membered, t31_zfmisc_1, cc4_tex_2, cc8_tex_2, t59_tex_4, t58_partfun1, t88_tex_4, t19_funcop_1, d1_zfmisc_1, t16_xboole_1, t4_t_0topsp, cc2_tops_1, t51_pre_topc, t100_zfmisc_1, d2_pcomps_1, t21_tex_4, t26_xboole_1, t63_xboole_1, t11_tex_3, redefinition_k7_funcop_1, d3_tex_3, t7_tex_2, t74_tex_3, t57_borsuk_1, rc2_tex_3, t15_xboole_1, fc3_eqrel_1, t43_funct_2, commutativity_k4_subset_1, t15_tex_4, rc9_tex_2, fraenkel_a_3_0_pcomps_1, t91_partfun1, rc2_relat_1, t82_tsep_1, dt_k5_subset_1, existence_m2_relset_1, t16_membered, t23_tex_3, d4_binop_1, t2_tex_2, t16_tops_2, t70_tex_3, dt_k9_funcop_1, t70_tops_2, t38_zfmisc_1, t43_tsep_1, t60_tops_2, t40_tex_4, t48_tops_1, redefinition_k7_subset_1, rc3_pcomps_1, cc36_tex_2, t34_funcop_1, cc32_tex_2, t65_borsuk_1, fraenkel_a_2_10_tex_4, t12_tsep_1, t43_tops_3, symmetry_r1_tsep_1, dt_k23_borsuk_1, t116_funct_2, t44_relat_2, t168_partfun1, t142_funct_1, t5_tsep_1, t26_tex_2, t27_borsuk_1, t69_funcop_1, t23_membered, t36_zfmisc_1, t157_relat_1, t96_tops_1, cc41_tex_2, t45_tops_1, s14_funct_2, t24_tsep_1, t6_tops_2, d9_pre_topc, fc46_membered, t26_tops_2, t25_tex_3, t24_tex_4, t26_subset_1, redefinition_k2_binop_1, t92_partfun1, t26_pcomps_1, t17_pre_topc, t68_tops_2, t73_partfun1, t82_partfun1, t51_subset_1, t21_subset_1, t2_tsep_1, dt_k7_funcop_1, t51_tops_1, d7_tsep_1, rc2_tsp_1, t22_xboole_1, t47_tex_4, t9_tex_2, t76_tops_3, involutiveness_k10_funcop_1, cc12_tex_2, t85_tops_1, fc4_funcop_1, dt_k13_borsuk_1, t6_funct_2, dt_m1_connsp_2, t21_pcomps_1, t41_subset_1, t18_tops_2, t26_membered, cc9_tsp_1, t94_partfun1, redefinition_k6_funcop_1, d3_tarski, t18_binop_1, d1_tsp_2, t15_membered, t50_tex_3, t42_funcop_1, t54_zfmisc_1, fc35_membered, t69_tex_4, cc26_tex_3, dt_k3_partfun1, t41_tex_2, t8_xboole_1, t71_tsep_1, t103_xboole_1, cc46_tex_2, t58_funcop_1, t36_tops_1, t37_relat_1, t6_relset_1, t78_xboole_1, t28_xboole_1, t16_borsuk_1, t82_borsuk_1, d1_relset_1, t28_pcomps_1, t81_borsuk_1, t74_partfun1, d7_tex_4, t46_subset_1, fc1_struct_0, t88_tsep_1, cc6_funct_2, t10_tsp_1, t19_tex_4, d2_tsep_1, redefinition_k1_struct_0, fc2_tex_2, existence_l1_pre_topc, t77_tsep_1, t60_subset_1, t39_zfmisc_1, d19_borsuk_1, t5_xboole_0, t131_funct_2, t119_zfmisc_1, d4_tsp_2, t5_tops_2, rc1_relat_1, t20_membered, t13_xboole_1, t60_relat_1, d3_tsep_1, t52_tex_4, t40_subset_1, d9_borsuk_1, t83_zfmisc_1, t170_relat_1, dt_k5_relat_1, t17_subset_1, reflexivity_r1_tarski, t9_funct_1, d4_t_0topsp, s3_subset_1, fraenkel_a_2_4_tex_4, d10_tsp_1, t17_tex_4, t83_tex_4, fc36_membered, cc3_tex_3, t37_funcop_1, t22_connsp_2, t54_tex_3, d1_funct_2, t6_zfmisc_1, dt_k14_borsuk_1, t48_relat_1, dt_k10_relset_1, t2_tops_3, t12_eqrel_1, t75_tops_3, t55_tex_3, dt_k1_tsp_2, t143_funct_2, t47_tex_2, t55_tsep_1, t33_borsuk_1, t18_funct_2, t144_funct_1, redefinition_m1_struct_0, t121_zfmisc_1, t10_subset_1, t41_tex_3, fc1_pcomps_1, dt_l2_struct_0, redefinition_m1_tsp_1, t72_tops_3, d1_connsp_2, redefinition_k1_partfun1, t17_tsep_1, rc3_tex_3, t2_xboole_1, t55_tex_4, cc7_tex_4, t9_tex_4, t4_xboole_1, t57_partfun1, t141_partfun1, fc15_tex_4, cc21_tex_2, fc13_tops_1, cc17_membered, d12_funct_1, t9_relset_1, t65_tex_4, fraenkel_a_2_0_tex_2, fc2_tex_4, dt_k4_borsuk_1, t59_zfmisc_1, fc6_relat_1, t1_partfun1, t150_funct_1, rc1_pre_topc, t13_connsp_2, t28_membered, t57_subset_1, t93_tsep_1, t47_zfmisc_1, d15_binop_1, t8_tops_3, d5_tex_4, rc13_tex_2, t28_tex_4, t63_tex_4, t69_tex_3, t18_zfmisc_1, t29_membered, d5_tops_3, redefinition_v2_tsp_1, t25_connsp_2, t20_relat_1, t31_tops_1, rc7_pre_topc, t47_tsep_1, t51_relat_1, t61_tex_4, t84_partfun1, d2_tsp_1, t45_borsuk_1, t20_tops_1, t113_partfun1, cc28_tex_2, dt_k8_eqrel_1, t46_relat_1, dt_k2_tops_2, cc23_tex_2, d4_tex_2, t58_tops_2, d18_tex_4, t84_tex_4, redefinition_k9_borsuk_1, t40_tsep_1, redefinition_k7_relset_1, t45_tex_3, t17_tops_3, t17_funcop_1, t53_tops_1, t48_borsuk_1, d15_tex_4, rc3_borsuk_1, fc3_pre_topc, d6_eqrel_1, cc13_tex_2, t85_tops_3, t68_tsep_1, redefinition_k11_relset_1, existence_m1_eqrel_1, t56_tops_3, t51_zfmisc_1, cc17_tex_2, dt_k8_subset_1, t73_tops_2, fraenkel_a_2_6_tex_4, t49_pre_topc, redefinition_k8_borsuk_1, t94_xboole_1, t17_t_0topsp, t47_subset_1, t2_tsp_1, t151_funct_2, t20_tsep_1, t127_zfmisc_1, t52_tsep_1, d3_pcomps_1, t136_zfmisc_1, t11_xboole_1, fc7_tops_1, cc50_tex_2, t62_tops_2, d2_t_0topsp, dt_k2_pcomps_1, d5_binop_1, d9_pcomps_1, cc30_tex_2, dt_m2_subset_1, dt_k5_numbers, d9_tex_4, rc9_tex_3, t27_eqrel_1, t51_relset_1, cc12_tex_3, t19_borsuk_1, t1_tops_2, t12_funct_2, d16_binop_1, t54_subset_1, t59_tex_2, t39_pre_topc, t64_xboole_1, fc4_borsuk_1, t22_pre_topc, t70_funcop_1, t72_tex_2, t50_relset_1, t44_subset_1, t42_tsep_1, redefinition_k5_pre_topc, rc2_tops_1, t35_partfun1, d8_binop_1, t10_pcomps_1, t93_xboole_1, cc5_tex_4, t21_funct_1, dt_k4_tex_4, t60_borsuk_1, t68_tex_4, t69_tops_3, t5_membered, t58_tsep_1, fc1_relat_1, t77_xboole_1, redefinition_k2_struct_0, cc6_membered, t8_boole, t169_relat_1, cc13_tsp_1, rc1_xboole_0, t21_borsuk_1, t24_partfun1, redefinition_k8_funct_2, fc3_tops_1, t34_zfmisc_1, t80_zfmisc_1, dt_u1_pre_topc, fc3_funct_1, t47_tops_1, t107_tops_1, t59_tops_3, d3_tsp_1, t5_relat_1, t24_zfmisc_1, t58_tex_3, rc2_tex_2, t22_membered, t48_pre_topc, t75_funcop_1, t156_relat_1, t53_zfmisc_1, cc48_tex_2, d5_borsuk_1, t64_tops_3, t51_tsep_1, rc1_tsp_1, t23_relat_1, cc4_tops_1, t6_tex_3, rc8_tex_2, rc5_struct_0, rc7_tex_2, t182_relat_1, t54_funcop_1, t120_funct_2, d1_borsuk_1, redefinition_k3_funct_2, t59_funct_2, cc20_tex_2, t12_xboole_1, rc4_borsuk_1, t10_zfmisc_1, t2_subset, dt_k5_pre_topc, fraenkel_a_2_2_tex_4, reflexivity_r1_partfun1, t38_funct_2, t33_partfun1, cc1_membered, d3_relat_1, t85_funct_2, fc1_tex_2, t64_tex_3, t44_tsep_1, t7_pcomps_1, t10_tsep_1, fc7_relat_1, t14_funcop_1, t180_relat_1, t20_pcomps_1, d6_borsuk_1, rc2_pcomps_1, t2_pcomps_1, d5_tsp_1, t1_tex_3, t37_zfmisc_1, fc2_relat_1, t65_relat_1, t21_relat_1, t6_connsp_2, t19_connsp_2, t31_tsep_1, t20_funcop_1, t45_tsep_1, t14_borsuk_1, t109_zfmisc_1, cc10_tsp_1, t152_relat_1, symmetry_r1_xboole_0, cc39_tex_2, t134_zfmisc_1, existence_m1_borsuk_1, t25_partfun1, t49_relat_1, t43_eqrel_1, t39_tex_3, t37_tex_2, t26_connsp_2, fc8_relat_1, t161_funct_1, t27_funct_1, d15_membered, t82_funcop_1, t74_tex_2, fc5_tex_4, dt_k3_binop_1, t40_relat_1, t70_tops_3, d4_tops_1, dt_l1_metric_1, t40_tops_1, t52_tops_3, dt_k1_tsep_1, t74_xboole_1, dt_k6_eqrel_1, d4_connsp_2, d18_binop_1, t18_membered, redefinition_k4_borsuk_1, fc3_tex_4, redefinition_k7_borsuk_1, t65_tops_3, t67_tex_3, t13_tsp_1, t115_funct_2, t66_tops_3, idempotence_k2_xboole_0, t59_tops_2, d3_tops_1, t36_tex_4, t48_subset_1, cc2_membered, t34_tex_4, t4_tex_4, dt_k1_pcomps_1, t58_borsuk_1, rc1_pcomps_1, d1_funct_1, t32_borsuk_1, dt_k1_t_0topsp, t62_tex_4, t15_pre_topc, t73_tex_2, cc42_tex_2, t57_tops_3, t115_partfun1, t15_t_0topsp, d12_pre_topc, fc14_tex_4, fc2_funcop_1, t9_tarski, t1_tops_3, t145_relat_1, rc2_borsuk_1, cc24_tex_3, t89_tsep_1, t35_pcomps_1, t59_tsep_1, cc3_membered, t50_subset_1, t55_borsuk_1, rc2_pre_topc, t107_xboole_1, cc45_tex_2, d10_xboole_0, t21_tex_3, t1_tex_2, fc18_tex_4, fc8_tex_4, cc5_tsp_1, t71_borsuk_1, t44_tex_4, t149_relat_1, t50_tops_2, t7_xboole_1, cc1_tex_4, d15_borsuk_1, redefinition_k20_borsuk_1, redefinition_k5_relset_1, t3_xboole_0, t46_tsep_1, t77_funcop_1, t33_tops_3, t29_tex_3, t80_tops_3, existence_l1_struct_0, fc3_funcop_1, t5_xboole_1, t79_tex_2, t74_tops_1, t49_subset_1, fc1_funcop_1, t44_funcop_1, rc1_tsep_1, t7_tarski, t50_tex_2, t15_borsuk_1, t33_funct_1, t145_funct_2, t78_tex_2, t34_pcomps_1, t70_tex_4, t66_borsuk_1, t19_tops_2, rc1_partfun1, t57_tex_2, d20_borsuk_1, t75_tex_4, t159_funct_1, t42_eqrel_1, t34_tex_2, t19_tsp_1, t27_partfun1, symmetry_r1_partfun1, t91_xboole_1, t43_tops_2, t67_partfun1, t33_tex_3, d5_funct_1, t6_ordinal1, t1_tsep_1, t93_zfmisc_1, t5_connsp_2, d13_tsp_1, t56_tops_2, t12_relset_1, redefinition_k4_relset_1, fc4_tex_2, cc5_funct_2, t25_pcomps_1, t48_relset_1, redefinition_m2_subset_1, t1_tex_4, redefinition_k1_borsuk_1, t36_tops_3, d7_t_0topsp, t31_tex_3, t24_membered, existence_l1_metric_1, t59_funcop_1, t25_relat_1, d1_tops_1, t22_funct_2, d10_membered, cc34_tex_2, t5_tsp_1, t13_binop_1, d13_tex_4, t6_tsp_1, rc1_tex_2, t109_tops_1, t11_tsep_1, cc32_tex_3, t72_funcop_1, t26_partfun1, t30_zfmisc_1, rc5_pre_topc, t32_eqrel_1, rc4_struct_0, t16_tex_2, t28_connsp_2, cc16_membered, t39_borsuk_1, t16_binop_1, t79_tsep_1, t139_partfun1, cc3_tsp_1, d13_binop_1, t38_tex_2, idempotence_k4_subset_1, t5_pcomps_1, t143_partfun1, cc25_tex_3, t22_tops_3, d1_binop_1, t43_tex_2, dt_m1_tsp_1, dt_u1_metric_1, fc22_membered, rc2_xboole_0, d8_tops_1, t24_pre_topc, t14_tex_2, t26_tops_1, t174_partfun1, t27_relat_2, t80_partfun1, t55_funct_2, t66_relat_1, t38_partfun1, t32_tex_4, t44_tops_1, fc27_membered, fc4_pcomps_1, t27_tex_4, dt_k3_pre_topc, d1_pre_topc, fc9_tex_4, t67_funct_2, dt_k6_pre_topc, cc12_tsp_1, d6_tsp_1, d2_borsuk_1, fc16_tex_4, t112_zfmisc_1, d3_tex_2, t63_tops_3, t78_partfun1, t2_xboole_0, t159_relat_1, t30_partfun1, fc13_tex_4, antisymmetry_r2_hidden, t68_tops_1, t21_tops_1, dt_k2_pre_topc, t61_funct_2, t24_tops_3, t10_xboole_1, d3_binop_1, t28_funct_2, t35_tex_4, dt_k3_subset_1, fc1_funct_2, t26_tex_3, fc23_membered, t46_tops_3, t38_tops_2, cc1_binop_1, t6_relat_1, t73_borsuk_1, t172_partfun1, t33_subset_1, t49_tex_4, t18_tops_3, t31_borsuk_1, t48_tops_2, t19_membered, t29_tops_3, t11_eqrel_1, cc6_tex_2, t14_pre_topc, redefinition_k9_funcop_1, t29_tops_1, t63_subset_1, t112_partfun1, d3_xboole_0, d20_membered, t12_pcomps_1, t66_tex_2, d9_tsep_1, d2_relat_1, t56_tex_4, t94_tops_1, t23_funcop_1, t11_pcomps_1, t42_pre_topc, t23_relset_1, d7_tsp_1, cc27_tex_2, d19_binop_1, t26_relat_1, t82_tex_4, redefinition_k4_tex_4, cc1_pre_topc, t167_relat_1, d2_tex_3, t69_borsuk_1, t22_subset_1
% 129.91/33.40 % No. of inferences in proof: 4354
% 129.91/33.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32864 ms resp. 32202 ms w/o parsing
% 132.84/34.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 132.84/34.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------