TSTP Solution File: TOP042+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : TOP042+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 12:38:59 EDT 2023
% Result : Theorem 8.61s 2.89s
% Output : Refutation 8.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 166
% Syntax : Number of formulae : 281 ( 21 unt; 53 typ; 0 def)
% Number of atoms : 1176 ( 36 equ; 0 cnn)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 3249 ( 226 ~; 2 |; 582 &;2075 @)
% ( 6 <=>; 358 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 2 con; 0-4 aty)
% Number of variables : 449 ( 0 ^; 406 !; 43 ?; 449 :)
% 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(v2_tsp_2_type,type,
v2_tsp_2: $i > $i > $o ).
thf(m2_tsp_1_type,type,
m2_tsp_1: $i > $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(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(k4_tsp_2_type,type,
k4_tsp_2: $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(m1_pre_topc_type,type,
m1_pre_topc: $i > $i > $o ).
thf(v2_tex_2_type,type,
v2_tex_2: $i > $i > $o ).
thf(v1_borsuk_1_type,type,
v1_borsuk_1: $i > $i > $o ).
thf(v2_t_0topsp_type,type,
v2_t_0topsp: $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(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(v2_tops_1_type,type,
v2_tops_1: $i > $i > $o ).
thf(v3_pre_topc_type,type,
v3_pre_topc: $i > $i > $o ).
thf(v1_tsep_1_type,type,
v1_tsep_1: $i > $i > $o ).
thf(v1_tdlat_3_type,type,
v1_tdlat_3: $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(v2_tdlat_3_type,type,
v2_tdlat_3: $i > $o ).
thf(v3_tdlat_3_type,type,
v3_tdlat_3: $i > $o ).
thf(v1_xcmplx_0_type,type,
v1_xcmplx_0: $i > $o ).
thf(v4_ordinal2_type,type,
v4_ordinal2: $i > $o ).
thf(v1_xreal_0_type,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_type,type,
v1_rat_1: $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k3_tex_4_type,type,
k3_tex_4: $i > $i > $i ).
thf(k1_tsp_2_type,type,
k1_tsp_2: $i > $i > $i ).
thf(v5_pre_topc_type,type,
v5_pre_topc: $i > $i > $i > $o ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(v3_tops_1_type,type,
v3_tops_1: $i > $i > $o ).
thf(v1_tex_3_type,type,
v1_tex_3: $i > $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(69,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(384,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)],[69]) ).
thf(25,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(225,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(8,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(138,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(91,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m2_tsp_1 @ 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 ) ) )
=> ( ( C
= ( k4_tsp_2 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D
= ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k3_tex_4 @ A @ E ) )
= ( k4_pre_topc @ A @ B @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_tsp_2) ).
thf(468,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m2_tsp_1 @ 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 ) ) )
=> ( ( ( C
= ( k4_tsp_2 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D
= ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k3_tex_4 @ A @ E ) )
= ( k4_pre_topc @ A @ B @ C @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D
= ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k3_tex_4 @ A @ E ) )
= ( k4_pre_topc @ A @ B @ C @ E ) ) ) ) )
=> ( C
= ( k4_tsp_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(13,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(170,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)],[13]) ).
thf(114,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(582,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)],[114]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ ( k4_tsp_2 @ A @ B ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tsp_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ ( k4_tsp_2 @ A @ B ) @ C ) @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(115,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A )
& ( m2_tsp_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ C @ A )
=> ( v4_pre_topc @ ( k4_pre_topc @ A @ B @ ( k4_tsp_2 @ A @ B ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,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(308,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)],[45]) ).
thf(31,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(247,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(36,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(269,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(73,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(404,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)],[73]) ).
thf(77,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(417,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)],[77]) ).
thf(41,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ 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_tsp_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tsp_2) ).
thf(288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ 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_tsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,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(320,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)],[50]) ).
thf(110,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(570,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)],[110]) ).
thf(3,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(125,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)],[3]) ).
thf(61,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(357,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)],[61]) ).
thf(107,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(559,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)],[107]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(228,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(87,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(448,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)],[87]) ).
thf(93,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(492,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)],[93]) ).
thf(21,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(211,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)],[21]) ).
thf(29,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(238,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)],[29]) ).
thf(58,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(348,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)],[58]) ).
thf(92,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(480,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)],[92]) ).
thf(38,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(280,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)],[38]) ).
thf(23,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(221,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(88,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(453,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)],[88]) ).
thf(5,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(132,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,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(265,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)],[35]) ).
thf(100,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(527,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(101,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_tsp_2) ).
thf(529,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(18,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(201,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(381,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(74,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(407,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m2_tsp_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(429,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(99,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(522,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)],[99]) ).
thf(40,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tsp_2) ).
thf(285,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(11,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(156,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)],[11]) ).
thf(16,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(188,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)],[16]) ).
thf(70,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(388,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)],[70]) ).
thf(78,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(420,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)],[78]) ).
thf(96,axiom,
? [A: $i] : ( l1_pre_topc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(499,plain,
? [A: $i] : ( l1_pre_topc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(6,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(134,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,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(311,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)],[46]) ).
thf(43,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(298,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(10,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(149,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)],[10]) ).
thf(66,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_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tsp_2) ).
thf(375,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_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,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(423,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)],[79]) ).
thf(112,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(577,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)],[112]) ).
thf(19,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(204,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(104,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(545,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)],[104]) ).
thf(33,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_borsuk_1 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_tsp_2) ).
thf(259,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_borsuk_1 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(113,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tsp_2) ).
thf(579,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(42,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(291,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)],[42]) ).
thf(47,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(313,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)],[47]) ).
thf(54,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(335,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)],[54]) ).
thf(27,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(230,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)],[27]) ).
thf(30,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(245,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(49,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(318,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)],[49]) ).
thf(62,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(362,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)],[62]) ).
thf(109,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(567,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)],[109]) ).
thf(37,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(271,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)],[37]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(208,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(94,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(494,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)],[94]) ).
thf(103,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(535,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)],[103]) ).
thf(51,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(323,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)],[51]) ).
thf(9,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(140,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)],[9]) ).
thf(98,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(520,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)],[98]) ).
thf(57,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(345,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)],[57]) ).
thf(64,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(367,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)],[64]) ).
thf(4,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(130,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)],[4]) ).
thf(24,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(223,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(84,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tsp_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tsp_2) ).
thf(438,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v2_tsp_2 @ B @ A )
=> ( ( v2_pre_topc @ B )
& ( v1_tex_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(82,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(431,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)],[82]) ).
thf(12,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(167,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(80,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(426,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)],[80]) ).
thf(56,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(342,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(105,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(553,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)],[105]) ).
thf(89,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(458,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)],[89]) ).
thf(17,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(194,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)],[17]) ).
thf(106,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(557,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(39,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(282,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)],[39]) ).
thf(76,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(414,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)],[76]) ).
thf(52,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(327,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)],[52]) ).
thf(75,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(409,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)],[75]) ).
thf(15,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(177,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)],[15]) ).
thf(53,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(331,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)],[53]) ).
thf(85,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(441,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(14,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(175,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(86,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(446,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)],[86]) ).
thf(32,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(250,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)],[32]) ).
thf(22,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(218,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(44,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(304,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(59,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(351,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(71,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(390,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)],[71]) ).
thf(72,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(401,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)],[72]) ).
thf(67,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tsp_2) ).
thf(378,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_tsp_2 @ B @ A ) )
=> ( ( v2_pre_topc @ B )
& ~ ( v1_tsep_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(28,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(235,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(83,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(433,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)],[83]) ).
thf(48,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(315,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)],[48]) ).
thf(34,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(262,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)],[34]) ).
thf(65,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(373,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)],[65]) ).
thf(108,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(564,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)],[108]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,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_tsp_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tsp_2) ).
thf(532,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_tsp_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(90,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(464,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)],[90]) ).
thf(111,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(575,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(97,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(501,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)],[97]) ).
thf(55,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(337,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)],[55]) ).
thf(60,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tsp_2) ).
thf(354,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v2_tsp_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v2_t_0topsp @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(95,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(496,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)],[95]) ).
thf(63,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(364,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)],[63]) ).
thf(601,plain,
$false,
inference(cvc4,[status(thm)],[384,225,138,468,170,582,115,308,247,269,404,417,288,320,570,125,357,559,228,448,492,211,238,348,480,280,221,453,132,265,527,529,201,381,407,429,522,285,156,188,388,420,499,134,311,298,149,375,423,577,204,545,259,579,291,313,335,230,245,318,362,567,271,208,494,535,323,140,520,345,367,130,223,438,431,167,426,342,553,458,194,557,282,414,327,409,177,331,441,175,446,250,218,304,351,390,401,378,235,433,315,262,373,564,136,532,464,575,501,337,354,496,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : TOP042+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n013.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 19:59:21 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.98/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.12 % [INFO] Parsing done (195ms).
% 1.54/1.13 % [INFO] Running in sequential loop mode.
% 2.06/1.32 % [INFO] eprover registered as external prover.
% 2.06/1.32 % [INFO] cvc4 registered as external prover.
% 2.06/1.33 % [INFO] Scanning for conjecture ...
% 2.24/1.41 % [INFO] Found a conjecture and 121 axioms. Running axiom selection ...
% 2.63/1.49 % [INFO] Axiom selection finished. Selected 112 axioms (removed 9 axioms).
% 2.84/1.59 % [INFO] Problem is first-order (TPTP FOF).
% 2.84/1.61 % [INFO] Type checking passed.
% 2.84/1.61 % [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 ...
% 8.61/2.88 % External prover 'cvc4' found a proof!
% 8.61/2.88 % [INFO] Killing All external provers ...
% 8.61/2.88 % Time passed: 2326ms (effective reasoning time: 1752ms)
% 8.61/2.88 % 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)>
% 8.61/2.89 % Axioms used in derivation (112): cc1_tsp_1, rc1_tops_1, cc6_tops_1, cc4_tsp_2, redefinition_m2_relset_1, cc1_tops_1, redefinition_k4_pre_topc, cc12_membered, cc10_tsp_2, cc8_tsp_1, cc5_tsp_2, idempotence_k3_xboole_0, redefinition_k5_subset_1, redefinition_m2_tsp_1, cc2_tsp_1, cc10_membered, rc3_tops_1, t1_subset, fc34_membered, cc6_tsp_2, fc4_subset_1, fc31_membered, dt_k4_tsp_2, rc1_membered, redefinition_k4_tsp_2, t2_boole, dt_m2_tsp_1, cc5_tops_1, cc3_tops_1, cc3_tsp_2, dt_m2_relset_1, idempotence_k5_subset_1, d12_tsp_2, commutativity_k3_xboole_0, fc28_membered, rc6_pre_topc, fc32_membered, fc30_membered, cc2_tsp_2, dt_l1_pre_topc, t6_boole, rc2_subset_1, rc5_tops_1, fc33_membered, t5_subset, cc19_membered, existence_m1_relset_1, commutativity_k5_subset_1, cc7_tsp_1, fc6_membered, rc4_tops_1, cc11_membered, dt_k4_pre_topc, cc6_tsp_1, t4_subset, cc11_tsp_1, cc20_membered, t7_boole, rc3_struct_0, fc1_subset_1, fc29_membered, rc1_subset_1, cc4_membered, dt_k3_tex_4, dt_m1_pre_topc, cc18_membered, existence_m2_tsp_1, existence_m1_pre_topc, t3_subset, cc1_relset_1, cc13_membered, existence_m1_subset_1, cc4_tsp_1, cc15_membered, cc2_tops_1, dt_k5_subset_1, existence_m2_relset_1, cc7_tsp_2, cc9_tsp_1, fc1_struct_0, existence_l1_pre_topc, fc35_membered, reflexivity_r1_tarski, dt_k1_tsp_2, fc36_membered, cc17_membered, rc7_pre_topc, d2_tsp_1, rc2_tops_1, t8_boole, cc13_tsp_1, t2_subset, cc1_membered, cc10_tsp_1, rc5_struct_0, cc4_tops_1, cc2_membered, t62_tex_4, cc3_membered, cc8_tsp_2, cc5_tsp_1, cc14_membered, existence_l1_struct_0, t1_tsep_1, cc9_tsp_2, cc16_membered, cc3_tsp_1, fc27_membered, cc12_tsp_1, cc1_tsp_2, antisymmetry_r2_hidden, cc1_pre_topc
% 8.61/2.89 % No. of inferences in proof: 228
% 8.61/2.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2326 ms resp. 1752 ms w/o parsing
% 8.92/2.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.92/2.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------