%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP034+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:52:31 AM UTC 2026
% Result : Theorem 258.18s 96.16s
% Output : Refutation 262.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 952
% Syntax : Number of formulae : 2423 ( 326 unt; 0 typ; 38 def)
% Number of atoms : 16771 (1234 equ; 0 cnn)
% Maximal formula atoms : 214 ( 6 avg)
% Number of connectives : 53138 (4547 ~;1305 |;7298 &;34521 @)
% ( 199 <=>;5268 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 173 ( 170 usr; 28 con; 0-4 aty)
% Number of variables : 5847 ( 21 ^;5476 !; 312 ?;5847 :)
% ( 0 !>; 0 ?*; 0 @-; 38 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_decl,type,
l1_pre_topc: $i > $o ).
thf(v2_tsp_2_decl,type,
v2_tsp_2: $i > $i > $o ).
thf(m2_tsp_1_decl,type,
m2_tsp_1: $i > $i > $o ).
thf(r1_borsuk_1_decl,type,
r1_borsuk_1: $i > $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v3_pre_topc_decl,type,
v3_pre_topc: $i > $i > $o ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(v2_tops_1_decl,type,
v2_tops_1: $i > $i > $o ).
thf(v3_compts_1_decl,type,
v3_compts_1: $i > $o ).
thf(v4_pre_topc_decl,type,
v4_pre_topc: $i > $i > $o ).
thf(k1_struct_0_decl,type,
k1_struct_0: $i > $i > $i ).
thf(m1_pre_topc_decl,type,
m1_pre_topc: $i > $i > $o ).
thf(k1_tops_1_decl,type,
k1_tops_1: $i > $i > $i ).
thf(v2_t_0topsp_decl,type,
v2_t_0topsp: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_tex_2_decl,type,
k1_tex_2: $i > $i > $i ).
thf(k5_tex_4_decl,type,
k5_tex_4: $i > $i > $i ).
thf(g1_pre_topc_decl,type,
g1_pre_topc: $i > $i > $i ).
thf(u1_pre_topc_decl,type,
u1_pre_topc: $i > $i ).
thf(v1_tsp_2_decl,type,
v1_tsp_2: $i > $i > $o ).
thf(v1_tops_1_decl,type,
v1_tops_1: $i > $i > $o ).
thf(v3_tdlat_3_decl,type,
v3_tdlat_3: $i > $o ).
thf(k6_pre_topc_decl,type,
k6_pre_topc: $i > $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(v4_tex_2_decl,type,
v4_tex_2: $i > $i > $o ).
thf(v5_tex_2_decl,type,
v5_tex_2: $i > $i > $o ).
thf(v3_tops_1_decl,type,
v3_tops_1: $i > $i > $o ).
thf(v1_tsep_1_decl,type,
v1_tsep_1: $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_pre_topc_decl,type,
k1_pre_topc: $i > $i ).
thf(v1_borsuk_1_decl,type,
v1_borsuk_1: $i > $i > $o ).
thf(v1_pre_topc_decl,type,
v1_pre_topc: $i > $o ).
thf(v3_tex_3_decl,type,
v3_tex_3: $i > $i > $o ).
thf(k2_pre_topc_decl,type,
k2_pre_topc: $i > $i ).
thf(v1_tops_3_decl,type,
v1_tops_3: $i > $i > $o ).
thf(v1_tex_4_decl,type,
v1_tex_4: $i > $i > $o ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(v1_tex_2_decl,type,
v1_tex_2: $i > $i > $o ).
thf(v4_tdlat_3_decl,type,
v4_tdlat_3: $i > $o ).
thf(m1_tsp_1_decl,type,
m1_tsp_1: $i > $i > $o ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(v1_tsp_1_decl,type,
v1_tsp_1: $i > $i > $o ).
thf(k7_tex_4_decl,type,
k7_tex_4: $i > $i > $i ).
thf(a_3_1_pcomps_1_decl,type,
a_3_1_pcomps_1: $i > $i > $i > $i ).
thf(v3_tex_2_decl,type,
v3_tex_2: $i > $i > $o ).
thf(k1_lopclset_decl,type,
k1_lopclset: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v3_tex_4_decl,type,
v3_tex_4: $i > $i > $o ).
thf(v1_tdlat_3_decl,type,
v1_tdlat_3: $i > $o ).
thf(r2_tsep_2_decl,type,
r2_tsep_2: $i > $i > $i > $o ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(k18_borsuk_1_decl,type,
k18_borsuk_1: $i > $i > $i > $i ).
thf(v2_tex_2_decl,type,
v2_tex_2: $i > $i > $o ).
thf(v1_tex_3_decl,type,
v1_tex_3: $i > $i > $o ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k16_borsuk_1_decl,type,
k16_borsuk_1: $i > $i > $i ).
thf(k17_borsuk_1_decl,type,
k17_borsuk_1: $i > $i > $i ).
thf(k2_t_0topsp_decl,type,
k2_t_0topsp: $i > $i ).
thf(a_1_0_lopclset_decl,type,
a_1_0_lopclset: $i > $i ).
thf(k6_tex_4_decl,type,
k6_tex_4: $i > $i > $i ).
thf(v4_tex_4_decl,type,
v4_tex_4: $i > $i > $o ).
thf(v6_compts_1_decl,type,
v6_compts_1: $i > $i > $o ).
thf(a_2_3_borsuk_1_decl,type,
a_2_3_borsuk_1: $i > $i > $i ).
thf(v2_tdlat_3_decl,type,
v2_tdlat_3: $i > $o ).
thf(v2_compts_1_decl,type,
v2_compts_1: $i > $o ).
thf(v2_pcomps_1_decl,type,
v2_pcomps_1: $i > $o ).
thf(k3_t_0topsp_decl,type,
k3_t_0topsp: $i > $i ).
thf(k4_t_0topsp_decl,type,
k4_t_0topsp: $i > $i ).
thf(k6_borsuk_1_decl,type,
k6_borsuk_1: $i > $i > $i ).
thf(k11_borsuk_1_decl,type,
k11_borsuk_1: $i > $i > $i > $i ).
thf(k15_borsuk_1_decl,type,
k15_borsuk_1: $i > $i ).
thf(v3_realset2_decl,type,
v3_realset2: $i > $o ).
thf(v4_tex_3_decl,type,
v4_tex_3: $i > $i > $o ).
thf(v2_borsuk_1_decl,type,
v2_borsuk_1: $i > $i > $o ).
thf(m1_borsuk_1_decl,type,
m1_borsuk_1: $i > $i > $o ).
thf(k21_borsuk_1_decl,type,
k21_borsuk_1: $i > $i > $i > $i ).
thf(k20_borsuk_1_decl,type,
k20_borsuk_1: $i > $i > $i > $i ).
thf(r4_tsep_2_decl,type,
r4_tsep_2: $i > $i > $i > $o ).
thf(k2_pcomps_1_decl,type,
k2_pcomps_1: $i > $i ).
thf(k1_pcomps_1_decl,type,
k1_pcomps_1: $i > $i ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k2_borsuk_1_decl,type,
k2_borsuk_1: $i > $i > $i ).
thf(r2_borsuk_1_decl,type,
r2_borsuk_1: $i > $i > $o ).
thf(k1_connsp_1_decl,type,
k1_connsp_1: $i > $i > $i ).
thf(k1_tdlat_1_decl,type,
k1_tdlat_1: $i > $i ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k2_tdlat_1_decl,type,
k2_tdlat_1: $i > $i ).
thf(k3_tdlat_1_decl,type,
k3_tdlat_1: $i > $i ).
thf(r3_tsep_1_decl,type,
r3_tsep_1: $i > $i > $i > $o ).
thf(r1_tsep_1_decl,type,
r1_tsep_1: $i > $i > $i > $o ).
thf(r4_tsep_1_decl,type,
r4_tsep_1: $i > $i > $i > $o ).
thf(k1_tsep_1_decl,type,
k1_tsep_1: $i > $i > $i > $i ).
thf(v2_tex_3_decl,type,
v2_tex_3: $i > $i > $o ).
thf(v5_tdlat_3_decl,type,
v5_tdlat_3: $i > $o ).
thf(l1_funcsdom_decl,type,
l1_funcsdom: $i > $o ).
thf(v5_compts_1_decl,type,
v5_compts_1: $i > $o ).
thf(k2_tsep_1_decl,type,
k2_tsep_1: $i > $i > $i > $i ).
thf(a_3_0_borsuk_1_decl,type,
a_3_0_borsuk_1: $i > $i > $i > $i ).
thf(v2_tsp_1_decl,type,
v2_tsp_1: $i > $i > $o ).
thf(k6_lopclset_decl,type,
k6_lopclset: $i > $i ).
thf(r3_tsep_2_decl,type,
r3_tsep_2: $i > $i > $i > $o ).
thf(v3_tsp_1_decl,type,
v3_tsp_1: $i > $i > $o ).
thf(k22_borsuk_1_decl,type,
k22_borsuk_1: $i ).
thf(a_1_0_t_0topsp_decl,type,
a_1_0_t_0topsp: $i > $i ).
thf(k19_borsuk_1_decl,type,
k19_borsuk_1: $i > $i > $i > $i ).
thf(a_2_2_borsuk_1_decl,type,
a_2_2_borsuk_1: $i > $i > $i ).
thf(v4_compts_1_decl,type,
v4_compts_1: $i > $o ).
thf(l2_quantal1_decl,type,
l2_quantal1: $i > $o ).
thf(k3_tsp_2_decl,type,
k3_tsp_2: $i > $i > $i ).
thf(k1_tsp_2_decl,type,
k1_tsp_2: $i > $i > $i ).
thf(v3_pcomps_1_decl,type,
v3_pcomps_1: $i > $o ).
thf(k4_tdlat_1_decl,type,
k4_tdlat_1: $i > $i ).
thf(k12_tdlat_1_decl,type,
k12_tdlat_1: $i > $i ).
thf(k8_tdlat_1_decl,type,
k8_tdlat_1: $i > $i ).
thf(k10_tdlat_1_decl,type,
k10_tdlat_1: $i > $i ).
thf(k11_tdlat_1_decl,type,
k11_tdlat_1: $i > $i ).
thf(k6_tdlat_1_decl,type,
k6_tdlat_1: $i > $i ).
thf(k7_tdlat_1_decl,type,
k7_tdlat_1: $i > $i ).
thf(k2_tsp_2_decl,type,
k2_tsp_2: $i > $i > $i ).
thf(k4_tsp_2_decl,type,
k4_tsp_2: $i > $i > $i ).
thf(v1_t_0topsp_decl,type,
v1_t_0topsp: $i > $i > $i > $o ).
thf(k9_tdlat_1_decl,type,
k9_tdlat_1: $i > $i ).
thf(k5_tdlat_1_decl,type,
k5_tdlat_1: $i > $i ).
thf(v17_lattices_decl,type,
v17_lattices: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk61_decl,type,
sk61: $i > $i > $i ).
thf(sk174_decl,type,
sk174: $i > $i ).
thf(sk175_decl,type,
sk175: $i > $i ).
thf(sk177_decl,type,
sk177: $i > $i > $i ).
thf(sk179_decl,type,
sk179: $i > $i ).
thf(sk204_decl,type,
sk204: $i > $i ).
thf(sk210_decl,type,
sk210: $i > $i ).
thf(sk212_decl,type,
sk212: $i > $i ).
thf(sk214_decl,type,
sk214: $i > $i ).
thf(sk220_decl,type,
sk220: $i ).
thf(sk238_decl,type,
sk238: $i ).
thf(sk239_decl,type,
sk239: $i ).
thf(sk249_decl,type,
sk249: $i ).
thf(sk255_decl,type,
sk255: $i ).
thf(sk264_decl,type,
sk264: $i ).
thf(sk281_decl,type,
sk281: $i ).
thf(sk289_decl,type,
sk289: $i ).
thf(sk290_decl,type,
sk290: $i ).
thf(sk298_decl,type,
sk298: $i ).
thf(sk308_decl,type,
sk308: $i ).
thf(sk320_decl,type,
sk320: $i ).
thf(sk324_decl,type,
sk324: $i ).
thf(sk325_decl,type,
sk325: $i ).
thf(sk326_decl,type,
sk326: $i ).
thf(sk327_decl,type,
sk327: $i ).
thf(sk328_decl,type,
sk328: $i ).
thf(sk329_decl,type,
sk329: $i ).
thf(sk330_decl,type,
sk330: $i ).
thf(sk334_decl,type,
sk334: $i ).
thf(sk336_decl,type,
sk336: $i ).
thf(sk337_decl,type,
sk337: $i ).
thf(sk338_decl,type,
sk338: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( sk1 @ ( A @ m2_tsp_1 ) )
& ( sk1 @ ( A @ v2_tsp_2 ) )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( sk1 @ r1_borsuk_1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( D @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( A @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( E @ v3_pre_topc ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( D @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( A @ r2_hidden ) )
& ~ ( E @ ( B @ r2_hidden ) )
& ( D @ ( E @ v3_pre_topc ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( B @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( B @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ ( A @ sk5 ) @ r2_hidden ) )
& ( B @ ( D @ v3_pre_topc ) ) ) )
& ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ ( A @ sk5 ) @ r2_hidden ) )
& ( B @ ( D @ v3_pre_topc ) ) ) )
& ( ( B @ ( A @ sk5 ) )
!= C )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ ( A @ sk5 ) @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk61_def,definition,
( sk61
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ) ) ).
thf(sk174_def,definition,
( sk174
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk175_def,definition,
( sk175
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk177_def,definition,
( sk177
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk179_def,definition,
( sk179
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk204_def,definition,
( sk204
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk210_def,definition,
( sk210
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_eqrel_1 ) ) ) ) ).
thf(sk212_def,definition,
( sk212
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk214_def,definition,
( sk214
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk220_def,definition,
( sk220
= ( @+[A: $i] : ( A @ l1_funcsdom ) ) ) ).
thf(sk238_def,definition,
( sk238
= ( @+[A: $i] :
( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk239_def,definition,
( sk239
= ( @+[A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk249_def,definition,
( sk249
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk255_def,definition,
( sk255
= ( @+[A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk264_def,definition,
( sk264
= ( @+[A: $i] :
( ( A @ v2_t_0topsp )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk281_def,definition,
( sk281
= ( @+[A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk289_def,definition,
( sk289
= ( @+[A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk290_def,definition,
( sk290
= ( @+[A: $i] :
( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk298_def,definition,
( sk298
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk308_def,definition,
( sk308
= ( @+[A: $i] : ( A @ l2_quantal1 ) ) ) ).
thf(sk320_def,definition,
( sk320
= ( @+[A: $i] :
( ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk324_def,definition,
( sk324
= ( @+[A: $i] :
( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk325_def,definition,
( sk325
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_quantal1 ) ) ) ) ).
thf(sk326_def,definition,
( sk326
= ( @+[A: $i] :
( ( A @ v3_pcomps_1 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk327_def,definition,
( sk327
= ( @+[A: $i] :
( ( A @ v2_pcomps_1 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk328_def,definition,
( sk328
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_funcsdom ) ) ) ) ).
thf(sk329_def,definition,
( sk329
= ( @+[A: $i] :
( ( A @ v3_compts_1 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk330_def,definition,
( sk330
= ( @+[A: $i] :
( ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk334_def,definition,
( sk334
= ( @+[A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk336_def,definition,
( sk336
= ( @+[A: $i] : ( A @ l1_pre_topc ) ) ) ).
thf(sk337_def,definition,
( sk337
= ( @+[A: $i] :
( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk338_def,definition,
( sk338
= ( @+[A: $i] :
( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(198,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ v4_pre_topc ) )
<=> ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_pre_topc) ).
thf(2163,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v4_pre_topc ) ) )
& ( ( B @ ( C @ v4_pre_topc ) )
=> ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(3471,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(3472,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3471]) ).
thf(3473,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[3472]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(3198,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(3199,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[3198]) ).
thf(3200,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[3199]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(3294,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(3295,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3294]) ).
thf(3296,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[3295]) ).
thf(12342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( A
= ( C @ ( D @ k3_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3200,3296]) ).
thf(12343,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
= A ),
inference(pattern_uni,[status(thm)],[12342:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ k2_xboole_0 ) ))]]) ).
thf(12351,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
= A ),
inference(simp,[status(thm)],[12343]) ).
thf(21728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ( ( C @ ( A @ ( B @ k2_xboole_0 ) @ k3_xboole_0 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3473,12351]) ).
thf(21729,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ k2_xboole_0 ) @ k3_xboole_0 ) )
= A ),
inference(pattern_uni,[status(thm)],[21728:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(792,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_tdlat_3 )
=> ( A @ v3_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tdlat_3) ).
thf(5469,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_tdlat_3 )
=> ( A @ v3_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(548,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_tex_3) ).
thf(3883,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(880,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp )
= ( A @ k2_t_0topsp @ ( A @ k16_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_t_0topsp) ).
thf(5918,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp )
= ( A @ k2_t_0topsp @ ( A @ k16_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(2889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(873,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ v2_pcomps_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v5_compts_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_pcomps_1) ).
thf(5896,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ v2_pcomps_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v5_compts_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(505,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_tops_2) ).
thf(3661,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(444,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(3398,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(3399,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(cnf,[status(esa)],[3398]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(3434,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(779,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ( A @ v5_tdlat_3 )
& ( A @ v4_tdlat_3 )
& ( A @ v3_tdlat_3 )
& ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tsp_1) ).
thf(5390,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ( A @ v5_tdlat_3 )
& ( A @ v4_tdlat_3 )
& ( A @ v3_tdlat_3 )
& ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(153,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( B @ ( D @ v3_pre_topc ) )
<=> ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tsep_1) ).
thf(1840,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
=> ( B @ ( D @ v3_pre_topc ) ) )
& ( ( B @ ( D @ v3_pre_topc ) )
=> ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_tsp_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(916,plain,
~ ! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(917,plain,
( ~ ( sk2 @ ( sk1 @ r1_borsuk_1 ) )
& ( sk1 @ ( sk2 @ m2_tsp_1 ) )
& ( sk1 @ ( sk2 @ v2_tsp_2 ) )
& ~ ( sk2 @ v3_struct_0 )
& ( sk1 @ l1_pre_topc )
& ( sk1 @ v2_pre_topc )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[916]) ).
thf(918,plain,
sk1 @ ( sk2 @ m2_tsp_1 ),
inference(cnfConj,[status(thm)],[917]) ).
thf(922,plain,
sk1 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[917]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( ( B @ v2_t_0topsp )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) )
| ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_tsp_1) ).
thf(953,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) )
| ( B @ v3_struct_0 ) )
=> ( B @ v2_t_0topsp ) )
& ( ( B @ v2_t_0topsp )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) )
| ( B @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(954,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ v2_t_0topsp )
| ~ ( F @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ( F @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ~ ( A @ ( F @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ( E @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ~ ( E @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ~ ( A @ ( E @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ( ( A @ ( B @ sk5 ) )
!= ( A @ ( B @ sk6 ) ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( B @ v2_t_0topsp )
| ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ) ),
inference(cnf,[status(esa)],[953]) ).
thf(956,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(7274,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,956]) ).
thf(7275,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[7274]) ).
thf(7276,plain,
! [A: $i] :
( ( A @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( sk1 @ ( A @ sk6 ) @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(pattern_uni,[status(thm)],[7275:[bind(A,$thf( sk1 ))]]) ).
thf(7424,plain,
! [A: $i] :
( ( A @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( sk1 @ ( A @ sk6 ) @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[7276]) ).
thf(919,plain,
sk1 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[917]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v3_compts_1 )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_pcomps_1) ).
thf(939,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v3_compts_1 )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v4_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( A @ v3_compts_1 )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[939]) ).
thf(6389,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ( A @ ( B @ ( A @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( A @ v3_compts_1 )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ $true
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[919,940]) ).
thf(6390,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ( A @ ( B @ ( A @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( A @ v3_compts_1 )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6389]) ).
thf(6391,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc )
| ( sk1 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[6390:[bind(A,$thf( sk1 ))]]) ).
thf(6436,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc )
| ( sk1 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6391]) ).
thf(924,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[917]) ).
thf(6482,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[6436,922,924]) ).
thf(6483,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6482]) ).
thf(7665,plain,
! [B: $i,A: $i] :
( ( ( A @ u1_struct_0 @ ( sk1 @ ( A @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ $true
| ( A @ v2_t_0topsp )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(paramod_ordered,[status(thm)],[7424,6483]) ).
thf(7666,plain,
! [B: $i,A: $i] :
( ( ( A @ u1_struct_0 @ ( sk1 @ ( A @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( A @ v2_t_0topsp )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[7665]) ).
thf(7667,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ v2_t_0topsp )
| ~ ( sk1 @ ( sk1 @ m2_tsp_1 ) ) ),
inference(pattern_uni,[status(thm)],[7666:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ ( sk1 @ sk6 ) ))]]) ).
thf(47335,plain,
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( sk1 @ ( sk1 @ m2_tsp_1 ) ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ v2_t_0topsp )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[918,7667]) ).
thf(47336,plain,
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( sk1 @ ( sk1 @ m2_tsp_1 ) ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[47335]) ).
thf(47413,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk1 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[47336]) ).
thf(47442,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk1 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[47413]) ).
thf(568,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc33_tex_2) ).
thf(4015,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(713,axiom,
? [A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tdlat_3) ).
thf(4990,plain,
? [A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(4991,plain,
( ( sk281 @ v3_tdlat_3 )
& ( sk281 @ v1_pre_topc )
& ( sk281 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[4990]) ).
thf(4992,plain,
sk281 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[4991]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v3_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_tsp_1) ).
thf(4904,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v3_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(227,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tex_2 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( B @ v4_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_tex_2) ).
thf(2306,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tex_2 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( B @ v4_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(858,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m2_tsp_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_tsp_1) ).
thf(5857,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m2_tsp_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(3053,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(582,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tex_3) ).
thf(4101,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(233,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_tops_1) ).
thf(2336,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(86,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ~ ( A @ ( B @ v1_tsp_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tsp_2) ).
thf(1454,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ~ ( A @ ( B @ v1_tsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_subset_1) ).
thf(1237,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(765,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc18_tex_2) ).
thf(5320,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(337,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(2918,plain,
! [A: $i] :
? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(2919,plain,
! [A: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( A @ sk175 @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[2918]) ).
thf(2921,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ sk175 @ v1_tex_2 ) ),
inference(cnfConj,[status(thm)],[2919]) ).
thf(469,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_tex_3) ).
thf(3477,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(308,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(2787,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(818,axiom,
? [A: $i] :
( ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tdlat_3) ).
thf(5671,plain,
? [A: $i] :
( ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(5672,plain,
( ( sk320 @ v2_tdlat_3 )
& ( sk320 @ v1_tdlat_3 )
& ( sk320 @ v1_pre_topc )
& ~ ( sk320 @ v3_struct_0 )
& ( sk320 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5671]) ).
thf(5676,plain,
sk320 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5672]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = B )
=> ( C @ ( D @ v4_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_tops_2) ).
thf(941,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = B )
=> ( C @ ( D @ v4_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(487,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_pcomps_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(3573,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_pcomps_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(3574,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_pcomps_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[3573]) ).
thf(401,axiom,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(3195,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(3196,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
inference(cnf,[status(esa)],[3195]) ).
thf(3197,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[3196]) ).
thf(8994,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ m1_subset_1 ) ),
inference(rewrite,[status(thm)],[3574,3197]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
thf(3663,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B != A )
=> ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) )
& ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(3664,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ( B = A )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( B != A )
| ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[3663]) ).
thf(3665,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[3664]) ).
thf(3667,plain,
! [B: $i,A: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[3665]) ).
thf(3668,plain,
! [A: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( A @ v1_tex_2 ) )
| ~ ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[3667]) ).
thf(9641,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8994,3668]) ).
thf(9642,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9641]) ).
thf(9643,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ v1_tex_2 ) ),
inference(pattern_uni,[status(thm)],[9642:[bind(A,$thf( C )),bind(B,$thf( C @ k1_zfmisc_1 ))]]) ).
thf(9676,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ v1_tex_2 ) ),
inference(simp,[status(thm)],[9643]) ).
thf(642,axiom,
? [A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tdlat_3) ).
thf(4519,plain,
? [A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v2_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(4520,plain,
( ( sk255 @ v3_tdlat_3 )
& ( sk255 @ v2_tdlat_3 )
& ( sk255 @ v1_tdlat_3 )
& ( sk255 @ v2_pre_topc )
& ( sk255 @ v1_pre_topc )
& ~ ( sk255 @ v3_struct_0 )
& ( sk255 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[4519]) ).
thf(4526,plain,
sk255 @ v2_tdlat_3,
inference(cnfConj,[status(thm)],[4520]) ).
thf(656,axiom,
? [A: $i] :
( ( A @ v2_t_0topsp )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tsp_1) ).
thf(4631,plain,
? [A: $i] :
( ( A @ v2_t_0topsp )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(4632,plain,
( ( sk264 @ v2_t_0topsp )
& ~ ( sk264 @ v2_tdlat_3 )
& ( sk264 @ v2_pre_topc )
& ( sk264 @ v1_pre_topc )
& ~ ( sk264 @ v3_realset2 )
& ~ ( sk264 @ v3_struct_0 )
& ( sk264 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[4631]) ).
thf(4633,plain,
~ ( sk264 @ v2_tdlat_3 ),
inference(cnfConj,[status(thm)],[4632]) ).
thf(6040,plain,
( ( ( sk264 @ v2_tdlat_3 )
!= ( sk255 @ v2_tdlat_3 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4526,4633]) ).
thf(6041,plain,
( ( sk264 @ v2_tdlat_3 )
!= ( sk255 @ v2_tdlat_3 ) ),
inference(simp,[status(thm)],[6040]) ).
thf(6042,plain,
sk264 != sk255,
inference(simp,[status(thm)],[6041]) ).
thf(829,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tsp_2) ).
thf(5733,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(874,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ l1_pre_topc )
& ( A @ k3_t_0topsp @ v2_t_0topsp )
& ( A @ k3_t_0topsp @ v2_pre_topc )
& ~ ( A @ k3_t_0topsp @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_t_0topsp) ).
thf(5898,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ l1_pre_topc )
& ( A @ k3_t_0topsp @ v2_t_0topsp )
& ( A @ k3_t_0topsp @ v2_pre_topc )
& ~ ( A @ k3_t_0topsp @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(2210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(752,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
<=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_tsep_1) ).
thf(5225,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(427,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ v2_tops_1 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_tops_3) ).
thf(3317,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ v2_tops_1 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_tops_1) ).
thf(1290,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D
= ( B @ u1_struct_0 @ ( C @ k3_xboole_0 ) ) )
& ( B @ ( D @ v4_pre_topc ) ) ) )
& ( A @ ( C @ v4_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tsp_1) ).
thf(2231,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D
= ( B @ u1_struct_0 @ ( C @ k3_xboole_0 ) ) )
& ( B @ ( D @ v4_pre_topc ) ) ) )
& ( A @ ( C @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(359,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
<=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_3) ).
thf(3040,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
=> ( A @ ( B @ v3_tops_1 ) ) )
& ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(867,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ v2_pcomps_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v4_compts_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_pcomps_1) ).
thf(5878,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ v2_pcomps_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v4_compts_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(376,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_tops_3) ).
thf(3108,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_3 ) )
=> ( A @ ( B @ v3_tops_1 ) ) )
& ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(189,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
<=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_tops_3) ).
thf(2114,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ k1_tops_1 ) @ v1_tops_1 ) )
=> ( A @ ( B @ v1_tops_3 ) ) )
& ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(612,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tex_3) ).
thf(4326,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(797,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tsep_1 ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_tdlat_3) ).
thf(5501,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tsep_1 ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(609,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) )
<=> ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tsep_1) ).
thf(4311,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_xboole_0 ) ) )
=> ( D
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B @ ( C @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tex_2) ).
thf(1522,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B @ ( C @ r1_tarski ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) )
& ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B @ ( C @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(289,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_tsp_1) ).
thf(2644,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(641,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_borsuk_1) ).
thf(4515,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(537,axiom,
? [A: $i] : ( A @ l1_funcsdom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_funcsdom) ).
thf(3812,plain,
? [A: $i] : ( A @ l1_funcsdom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(3813,plain,
sk220 @ l1_funcsdom,
inference(cnf,[status(esa)],[3812]) ).
thf(242,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( C
= ( B @ u1_struct_0 ) ) )
=> ( A @ ( C @ v1_tex_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_tex_4) ).
thf(2381,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( C
= ( B @ u1_struct_0 ) ) )
=> ( A @ ( C @ v1_tex_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(814,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
<=> ? [C: $i] :
( ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_tex_3) ).
thf(5644,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( A @ ( B @ v4_tex_3 ) ) )
& ( ( A @ ( B @ v4_tex_3 ) )
=> ? [C: $i] :
( ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(482,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( C @ ( A @ k1_connsp_1 ) @ ( D @ ( B @ k1_connsp_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_connsp_2) ).
thf(3549,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( C @ ( A @ k1_connsp_1 ) @ ( D @ ( B @ k1_connsp_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(305,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v1_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tdlat_3) ).
thf(2776,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ v1_tdlat_3 ) )
& ( ( A @ v1_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v4_pre_topc ) ) )
=> ( ( B @ ( E @ v4_pre_topc ) )
<=> ( A @ ( D @ v4_pre_topc ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tsep_1) ).
thf(1808,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v4_pre_topc ) ) )
=> ( ( ( A @ ( D @ v4_pre_topc ) )
=> ( B @ ( E @ v4_pre_topc ) ) )
& ( ( B @ ( E @ v4_pre_topc ) )
=> ( A @ ( D @ v4_pre_topc ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(291,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( ( B @ v2_t_0topsp )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ( C != D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) )
| ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_tsp_1) ).
thf(2659,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ( C != D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) )
| ( B @ v3_struct_0 ) )
=> ( B @ v2_t_0topsp ) )
& ( ( B @ v2_t_0topsp )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ( C != D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) )
| ( B @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(754,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_tsep_1) ).
thf(5242,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(113,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_borsuk_1) ).
thf(1618,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) )
=> ( A @ ( B @ v1_borsuk_1 ) ) )
& ( ( A @ ( B @ v1_borsuk_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(683,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v1_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_tex_3) ).
thf(4807,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v1_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(1544,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(842,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k8_tdlat_1 )
= ( A @ k12_tdlat_1 ) )
=> ( A @ v4_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_tdlat_3) ).
thf(5793,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k8_tdlat_1 )
= ( A @ k12_tdlat_1 ) )
=> ( A @ v4_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(141,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_tdlat_3) ).
thf(1793,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(3402,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(1533,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(655,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( B @ ( D @ v1_tops_3 ) )
<=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tex_3) ).
thf(4623,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
=> ( B @ ( D @ v1_tops_3 ) ) )
& ( ( B @ ( D @ v1_tops_3 ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(914,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_tsp_2) ).
thf(6031,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(769,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc25_tex_2) ).
thf(5348,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(910,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_tops_3) ).
thf(6017,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(893,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tsp_2) ).
thf(5967,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(900,axiom,
? [A: $i] :
( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_t_0topsp) ).
thf(5983,plain,
? [A: $i] :
( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(5984,plain,
( ( sk337 @ v2_t_0topsp )
& ( sk337 @ v2_pre_topc )
& ~ ( sk337 @ v3_struct_0 )
& ( sk337 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5983]) ).
thf(5988,plain,
sk337 @ v2_t_0topsp,
inference(cnfConj,[status(thm)],[5984]) ).
thf(755,axiom,
? [A: $i] :
( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tsp_1) ).
thf(5247,plain,
? [A: $i] :
( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(5248,plain,
( ~ ( sk290 @ v2_t_0topsp )
& ~ ( sk290 @ v1_tdlat_3 )
& ( sk290 @ v2_pre_topc )
& ( sk290 @ v1_pre_topc )
& ~ ( sk290 @ v3_realset2 )
& ~ ( sk290 @ v3_struct_0 )
& ( sk290 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5247]) ).
thf(5255,plain,
~ ( sk290 @ v2_t_0topsp ),
inference(cnfConj,[status(thm)],[5248]) ).
thf(6761,plain,
( ( ( sk337 @ v2_t_0topsp )
!= ( sk290 @ v2_t_0topsp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5988,5255]) ).
thf(6762,plain,
( ( sk337 @ v2_t_0topsp )
!= ( sk290 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[6761]) ).
thf(6764,plain,
sk337 != sk290,
inference(simp,[status(thm)],[6762]) ).
thf(525,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_pre_topc )
=> ( A
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(3745,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_pre_topc )
=> ( A
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(806,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_tdlat_3 )
=> ~ ( B @ v2_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc23_tex_2) ).
thf(5589,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_tdlat_3 )
=> ~ ( B @ v2_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ v2_tsp_1 ) )
<=> ( B @ v2_t_0topsp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v2_tsp_1) ).
thf(4097,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( ( B @ v2_t_0topsp )
=> ( A @ ( B @ v2_tsp_1 ) ) )
& ( ( A @ ( B @ v2_tsp_1 ) )
=> ( B @ v2_t_0topsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(360,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3044,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(257,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_struct_0 ) ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v3_tex_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_tex_4) ).
thf(2448,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_struct_0 ) ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v3_tex_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(4638,plain,
~ ( sk264 @ v3_realset2 ),
inference(cnfConj,[status(thm)],[4632]) ).
thf(47,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(1225,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1226,plain,
~ ? [A: $i,B: $i] :
( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[1225]) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1226]) ).
thf(9601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
!= ( C @ ( D @ r1_tarski ) ) )
| ~ $true
| ~ ( D @ ( C @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3399,1227]) ).
thf(9602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
!= ( C @ ( D @ r1_tarski ) ) )
| ~ ( D @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9601]) ).
thf(9603,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[9602:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ k2_xboole_0 ) )),bind(D,$thf( E ))]]) ).
thf(9613,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ k2_xboole_0 ) @ r2_hidden ) ),
inference(simp,[status(thm)],[9603]) ).
thf(15253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ~ ( C @ ( B @ ( A @ k2_xboole_0 ) @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3473,9613]) ).
thf(15254,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[15253:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( B @ ( D @ v4_pre_topc ) )
<=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tsep_1) ).
thf(1063,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
=> ( B @ ( D @ v4_pre_topc ) ) )
& ( ( B @ ( D @ v4_pre_topc ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B
!= ( A @ k1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_pre_topc) ).
thf(1354,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B
!= ( A @ k1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_subset_1) ).
thf(927,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( C @ ( B @ r1_tarski ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[927]) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[928]) ).
thf(88,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_tops_1) ).
thf(1458,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(736,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tex_3) ).
thf(5120,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(479,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v4_tex_4 ) )
& ~ ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tex_4) ).
thf(3530,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v4_tex_4 ) )
& ~ ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(534,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc39_tex_2) ).
thf(3794,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(3439,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(135,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_tex_3) ).
thf(1756,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(876,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v1_tdlat_3 )
=> ( B @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_tex_2) ).
thf(5906,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v1_tdlat_3 )
=> ( B @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).
thf(2035,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(431,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(3331,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(3332,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[3331]) ).
thf(833,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_tex_2) ).
thf(5755,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(584,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v3_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_tex_3) ).
thf(4110,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v3_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(594,axiom,
? [A: $i] :
( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tsp_1) ).
thf(4214,plain,
? [A: $i] :
( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(4215,plain,
( ~ ( sk238 @ v2_t_0topsp )
& ( sk238 @ v2_pre_topc )
& ( sk238 @ v1_pre_topc )
& ~ ( sk238 @ v3_realset2 )
& ~ ( sk238 @ v3_struct_0 )
& ( sk238 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[4214]) ).
thf(4220,plain,
~ ( sk238 @ v2_t_0topsp ),
inference(cnfConj,[status(thm)],[4215]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( B @ ( C @ ( A @ r1_tsep_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_tsep_1) ).
thf(4528,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( B @ ( C @ ( A @ r1_tsep_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(2184,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(5674,plain,
sk320 @ v2_tdlat_3,
inference(cnfConj,[status(thm)],[5672]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_tsp_1) ).
thf(1988,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(448,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tex_3) ).
thf(3414,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) )
=> ( A @ ( B @ v1_tex_3 ) ) )
& ( ( A @ ( B @ v1_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ v4_pre_topc ) )
| ( D != B )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ ( B @ v4_pre_topc ) )
| ~ ( A @ ( C @ m1_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[941]) ).
thf(943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ v4_pre_topc ) )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ ( B @ v4_pre_topc ) )
| ~ ( A @ ( C @ m1_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ( D != B ) ),
inference(lifteq,[status(thm)],[942]) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ v4_pre_topc ) )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ ( B @ v4_pre_topc ) )
| ~ ( A @ ( C @ m1_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[943]) ).
thf(6511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( C @ ( B @ v4_pre_topc ) )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ ( B @ v4_pre_topc ) )
| ~ ( A @ ( C @ m1_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,944]) ).
thf(6512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( C @ ( B @ v4_pre_topc ) )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ ( B @ v4_pre_topc ) )
| ~ ( A @ ( C @ m1_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6511]) ).
thf(6513,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ v4_pre_topc ) )
| ~ ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ v4_pre_topc ) )
| ~ ( sk1 @ ( B @ m1_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(pattern_uni,[status(thm)],[6512:[bind(A,$thf( sk1 ))]]) ).
thf(6551,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ v4_pre_topc ) )
| ~ ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ v4_pre_topc ) )
| ~ ( sk1 @ ( B @ m1_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6513]) ).
thf(716,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_tex_3) ).
thf(5005,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(275,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
<=> ( A @ v1_tdlat_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_tex_2) ).
thf(2580,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
=> ( ( ( A @ v1_tdlat_3 )
=> ( A @ ( B @ v3_tex_2 ) ) )
& ( ( A @ ( B @ v3_tex_2 ) )
=> ( A @ v1_tdlat_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
thf(945,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(426,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v2_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tex_4 ) )
& ( C
= ( B @ u1_struct_0 ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_tex_4) ).
thf(3313,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v2_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tex_4 ) )
& ( C
= ( B @ u1_struct_0 ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(3103,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(151,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ v1_tex_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tex_4) ).
thf(1835,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ v1_tex_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(830,axiom,
? [A: $i] :
( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_tdlat_3) ).
thf(5737,plain,
? [A: $i] :
( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(5738,plain,
( ( sk324 @ v5_tdlat_3 )
& ( sk324 @ v2_pre_topc )
& ( sk324 @ v1_pre_topc )
& ~ ( sk324 @ v3_struct_0 )
& ( sk324 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5737]) ).
thf(5740,plain,
sk324 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5738]) ).
thf(5252,plain,
sk290 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5248]) ).
thf(897,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_tdlat_3 )
=> ( A @ v2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tdlat_3) ).
thf(5977,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_tdlat_3 )
=> ( A @ v2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(884,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k4_tdlat_1 )
= ( A @ k12_tdlat_1 ) )
=> ( A @ v4_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_tdlat_3) ).
thf(5935,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k4_tdlat_1 )
= ( A @ k12_tdlat_1 ) )
=> ( A @ v4_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(881,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( A @ ( C @ v2_tsp_2 ) )
& ( C @ ( B @ m2_tsp_1 ) )
& ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tsp_2) ).
thf(5921,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( A @ ( C @ v2_tsp_2 ) )
& ( C @ ( B @ m2_tsp_1 ) )
& ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(682,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tex_3) ).
thf(4803,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v3_realset2 )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tex_2) ).
thf(3466,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v3_realset2 )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(92,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_tex_2) ).
thf(1475,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(865,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ v3_compts_1 )
=> ( B @ v3_compts_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_topmetr) ).
thf(5874,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ v3_compts_1 )
=> ( B @ v3_compts_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(249,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
& ( B != C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_tsp_1) ).
thf(2405,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
& ( B != C ) ) ) )
=> ( A @ v2_t_0topsp ) )
& ( ( A @ v2_t_0topsp )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
& ( B != C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k5_tex_4 ) @ m1_pre_topc ) )
& ( B @ ( A @ k5_tex_4 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_tex_4) ).
thf(1228,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k5_tex_4 ) @ m1_pre_topc ) )
& ( B @ ( A @ k5_tex_4 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(677,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tex_3) ).
thf(4775,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) )
=> ( A @ ( B @ v4_tex_3 ) ) )
& ( ( A @ ( B @ v4_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(770,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ( A @ v2_compts_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v4_compts_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_compts_1) ).
thf(5352,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ( A @ v2_compts_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v4_compts_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2957,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(303,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_tex_2) ).
thf(2763,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k19_borsuk_1 ) ) @ m1_borsuk_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_borsuk_1) ).
thf(5486,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k19_borsuk_1 ) ) @ m1_borsuk_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(139,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_borsuk_1) ).
thf(1782,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(578,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v1_tdlat_3 )
=> ( B @ v3_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_tex_2) ).
thf(4079,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v1_tdlat_3 )
=> ( B @ v3_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(603,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_borsuk_1) ).
thf(4266,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(523,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ ( A @ r1_tsep_1 ) ) )
& ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_tsep_1) ).
thf(3730,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ ( A @ r1_tsep_1 ) ) )
& ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ ( A @ r1_tsep_1 ) ) )
& ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(850,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v2_pre_topc )
=> ~ ( B @ v1_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_tex_2) ).
thf(5825,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v2_pre_topc )
=> ~ ( B @ v1_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(885,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k3_t_0topsp @ ( A @ ( A @ k4_t_0topsp @ v1_t_0topsp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_t_0topsp) ).
thf(5938,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k3_t_0topsp @ ( A @ ( A @ k4_t_0topsp @ v1_t_0topsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(836,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_funcsdom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funcsdom) ).
thf(5768,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_funcsdom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(5769,plain,
( ~ ( sk328 @ v3_struct_0 )
& ( sk328 @ l1_funcsdom ) ),
inference(cnf,[status(esa)],[5768]) ).
thf(5770,plain,
sk328 @ l1_funcsdom,
inference(cnfConj,[status(thm)],[5769]) ).
thf(552,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
<=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_tdlat_3 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) )
& ( B @ v1_tdlat_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_tex_2) ).
thf(3898,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_tdlat_3 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) )
& ( B @ v1_tdlat_3 ) )
=> ( A @ ( B @ v5_tex_2 ) ) )
& ( ( A @ ( B @ v5_tex_2 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_tdlat_3 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) )
& ( B @ v1_tdlat_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(182,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k6_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_tex_4) ).
thf(2082,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k6_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(248,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( A @ ( C @ v1_tsp_2 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tsp_2) ).
thf(2400,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( A @ ( C @ v1_tsp_2 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(832,axiom,
? [A: $i] :
( ( A @ v3_pcomps_1 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_pcomps_1) ).
thf(5748,plain,
? [A: $i] :
( ( A @ v3_pcomps_1 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(5749,plain,
( ( sk326 @ v3_pcomps_1 )
& ( sk326 @ v2_pre_topc )
& ( sk326 @ v1_pre_topc )
& ~ ( sk326 @ v3_struct_0 )
& ( sk326 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5748]) ).
thf(5750,plain,
sk326 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5749]) ).
thf(123,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tex_3) ).
thf(1703,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_tops_1) ).
thf(1709,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(840,axiom,
? [A: $i] :
( ( A @ v3_compts_1 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_pcomps_1) ).
thf(5783,plain,
? [A: $i] :
( ( A @ v3_compts_1 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(5784,plain,
( ( sk329 @ v3_compts_1 )
& ( sk329 @ v2_pre_topc )
& ( sk329 @ v1_pre_topc )
& ~ ( sk329 @ v3_struct_0 )
& ( sk329 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5783]) ).
thf(5788,plain,
sk329 @ v3_compts_1,
inference(cnfConj,[status(thm)],[5784]) ).
thf(6484,plain,
! [A: $i] :
( ( ( sk329 @ v3_compts_1 )
!= ( sk1 @ v3_compts_1 ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ $true
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[5788,6483]) ).
thf(6485,plain,
! [A: $i] :
( ( ( sk329 @ v3_compts_1 )
!= ( sk1 @ v3_compts_1 ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6484]) ).
thf(6486,plain,
! [A: $i] :
( ( sk329 != sk1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[6485]) ).
thf(7694,plain,
! [B: $i,A: $i] :
( ( ( A @ u1_struct_0 @ ( sk1 @ ( A @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ~ $true
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( A @ v2_t_0topsp )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(paramod_ordered,[status(thm)],[7424,6486]) ).
thf(7695,plain,
! [B: $i,A: $i] :
( ( ( A @ u1_struct_0 @ ( sk1 @ ( A @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( A @ v2_t_0topsp )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[7694]) ).
thf(7696,plain,
( ( sk329 != sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk1 @ v2_t_0topsp )
| ~ ( sk1 @ ( sk1 @ m2_tsp_1 ) ) ),
inference(pattern_uni,[status(thm)],[7695:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ ( sk1 @ sk6 ) ))]]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_borsuk_1) ).
thf(2755,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(365,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tex_3) ).
thf(3061,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(3485,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(148,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(1826,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(742,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
<=> ( C @ ( B @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tsep_1) ).
thf(5160,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( C @ ( B @ m1_pre_topc ) )
=> ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
& ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( C @ ( B @ m1_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(746,axiom,
! [A: $i] :
( ( A @ k2_pcomps_1 @ v2_pre_topc )
& ( A @ k2_pcomps_1 @ v1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_pcomps_1) ).
thf(5179,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ v2_pre_topc )
& ( A @ k2_pcomps_1 @ v1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(5180,plain,
( ! [A: $i] : ( A @ k2_pcomps_1 @ v2_pre_topc )
& ! [A: $i] : ( A @ k2_pcomps_1 @ v1_pre_topc ) ),
inference(miniscope,[status(thm)],[5179]) ).
thf(5181,plain,
! [B: $i,A: $i] :
( ( B @ k2_pcomps_1 @ v2_pre_topc )
& ( A @ k2_pcomps_1 @ v1_pre_topc ) ),
inference(cnf,[status(esa)],[5180]) ).
thf(5182,plain,
! [A: $i] : ( A @ k2_pcomps_1 @ v1_pre_topc ),
inference(cnfConj,[status(thm)],[5181]) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(7944,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ $true
| ~ ( A @ l1_pre_topc ) ),
inference(paramod_ordered,[status(thm)],[918,959]) ).
thf(7945,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[7944]) ).
thf(7946,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[7945:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(9189,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7946,922]) ).
thf(9190,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[9189]) ).
thf(9228,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ~ $true
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk2 @ v2_t_0topsp ) ),
inference(paramod_ordered,[status(thm)],[9190,6486]) ).
thf(9229,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk2 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[9228]) ).
thf(9230,plain,
( ( sk329 != sk1 )
| ( sk1 @ ( sk1 @ ( sk2 @ sk5 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk2 @ v2_t_0topsp ) ),
inference(pattern_uni,[status(thm)],[9229:[bind(A,$thf( sk1 @ ( sk2 @ sk5 ) ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( ( D @ ( A @ k1_tops_1 ) )
= ( E @ ( B @ k1_tops_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_tops_3) ).
thf(949,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( ( D @ ( A @ k1_tops_1 ) )
= ( E @ ( B @ k1_tops_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4637,plain,
sk264 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[4632]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(1409,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(888,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_tdlat_1 )
= ( A @ k9_tdlat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tdlat_3) ).
thf(5953,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_tdlat_1 )
= ( A @ k9_tdlat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(562,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_tsep_1) ).
thf(3976,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(281,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_tops_3) ).
thf(2603,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(4524,plain,
sk255 @ v1_tdlat_3,
inference(cnfConj,[status(thm)],[4520]) ).
thf(708,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
<=> ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_tsep_1) ).
thf(4956,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( C @ ( B @ m1_pre_topc ) ) )
& ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_t_0topsp )
<=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tsp_1) ).
thf(1660,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) )
=> ( A @ v2_t_0topsp ) )
& ( ( A @ v2_t_0topsp )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ v1_tex_2 ) )
& ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tex_4) ).
thf(2339,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ v1_tex_2 ) )
& ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(3045,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3044]) ).
thf(3046,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3045]) ).
thf(627,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v4_tex_3 ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ~ ( ( ( D @ ( C @ ( A @ k1_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ ( A @ r1_tsep_1 ) ) ) ) ) )
& ~ ( ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_tex_3) ).
thf(4415,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v4_tex_3 ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ~ ( ( ( D @ ( C @ ( A @ k1_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ ( A @ r1_tsep_1 ) ) ) ) ) )
& ~ ( ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(834,axiom,
? [A: $i] :
( ( A @ v2_pcomps_1 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pcomps_1) ).
thf(5757,plain,
? [A: $i] :
( ( A @ v2_pcomps_1 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(5758,plain,
( ( sk327 @ v2_pcomps_1 )
& ( sk327 @ v2_pre_topc )
& ~ ( sk327 @ v3_struct_0 )
& ( sk327 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5757]) ).
thf(5759,plain,
sk327 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5758]) ).
thf(659,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc48_tex_2) ).
thf(4654,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v1_tsp_1 ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v1_tsp_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tsp_1) ).
thf(1264,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v1_tsp_1 ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v1_tsp_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_pcomps_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( D @ ( E @ r1_xboole_0 ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_pcomps_1) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ~ ( D @ ( E @ r1_xboole_0 ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_pcomps_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_pcomps_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( D @ ( E @ r1_xboole_0 ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(3148,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(503,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(3652,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(3653,plain,
! [A: $i] : ( A @ ( A @ sk210 @ m1_eqrel_1 ) ),
inference(cnf,[status(esa)],[3652]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
& ( B != C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tsp_1) ).
thf(1313,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
& ( B != C ) ) ) )
=> ( A @ v2_t_0topsp ) )
& ( ( A @ v2_t_0topsp )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
& ( B != C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(605,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_tex_3) ).
thf(4275,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(931,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( B @ r1_xboole_0 ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( C @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[931]) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[932]) ).
thf(905,axiom,
? [A: $i] :
( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tsp_1) ).
thf(6000,plain,
? [A: $i] :
( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(6001,plain,
( ( sk338 @ v2_t_0topsp )
& ( sk338 @ v2_pre_topc )
& ( sk338 @ v1_pre_topc )
& ~ ( sk338 @ v3_struct_0 )
& ( sk338 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[6000]) ).
thf(6006,plain,
~ ( sk338 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6001]) ).
thf(901,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pre_topc ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pre_topc ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) )
=> ( E @ ( D @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_tsep_1) ).
thf(5989,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pre_topc ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pre_topc ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) )
=> ( E @ ( D @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(1132,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(544,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ~ ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v4_tex_3 ) )
& ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( ( A @ ( C @ v4_tex_3 ) )
| ( A @ ( B @ v4_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_tex_3) ).
thf(3855,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ~ ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v4_tex_3 ) )
& ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( ( A @ ( C @ v4_tex_3 ) )
| ( A @ ( B @ v4_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(831,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_quantal1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_quantal1) ).
thf(5744,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_quantal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(476,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_tsep_1) ).
thf(3517,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v4_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(105,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_tops_1) ).
thf(1572,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(794,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ~ ( ~ ( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) )
= ( C @ ( D @ ( A @ k2_tsep_1 ) ) @ ( B @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( D @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) )
& ~ ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ~ ( D @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_tsep_1) ).
thf(5480,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ~ ( ~ ( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) )
= ( C @ ( D @ ( A @ k2_tsep_1 ) ) @ ( B @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( D @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) )
& ~ ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ~ ( D @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(851,axiom,
? [A: $i] :
( ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_tdlat_3) ).
thf(5827,plain,
? [A: $i] :
( ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(5828,plain,
( ( sk330 @ v4_tdlat_3 )
& ( sk330 @ v2_pre_topc )
& ( sk330 @ v1_pre_topc )
& ~ ( sk330 @ v3_struct_0 )
& ( sk330 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5827]) ).
thf(5829,plain,
~ ( sk330 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5828]) ).
thf(5745,plain,
( ~ ( sk325 @ v3_struct_0 )
& ( sk325 @ l2_quantal1 ) ),
inference(cnf,[status(esa)],[5744]) ).
thf(5746,plain,
sk325 @ l2_quantal1,
inference(cnfConj,[status(thm)],[5745]) ).
thf(631,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k2_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_lopclset) ).
thf(4460,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k2_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(3180,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(676,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
<=> ( A @ ( C @ v2_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_tex_3) ).
thf(4771,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v2_tex_3 ) )
=> ( A @ ( B @ v4_tex_3 ) ) )
& ( ( A @ ( B @ v4_tex_3 ) )
=> ( A @ ( C @ v2_tex_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(811,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_t_0topsp )
& ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tsp_2) ).
thf(5617,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_t_0topsp )
& ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(160,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
<=> ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tsep_1) ).
thf(1922,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) )
& ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(907,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_tdlat_1 )
= ( A @ k5_tdlat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_tdlat_3) ).
thf(6010,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_tdlat_1 )
= ( A @ k5_tdlat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(1892,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(862,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_borsuk_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_borsuk_1) ).
thf(5868,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_borsuk_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(756,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_tex_3) ).
thf(5256,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(616,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( ( C @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( B @ ( D @ ( A @ r4_tsep_1 ) ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ r4_tsep_1 ) ) ) )
& ( ( ( D @ ( C @ ( A @ r4_tsep_1 ) ) )
& ( D @ ( B @ ( A @ r4_tsep_1 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_tsep_1) ).
thf(4353,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( ( C @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( B @ ( D @ ( A @ r4_tsep_1 ) ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ r4_tsep_1 ) ) ) )
& ( ( ( D @ ( C @ ( A @ r4_tsep_1 ) ) )
& ( D @ ( B @ ( A @ r4_tsep_1 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(861,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v2_t_0topsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tsp_1) ).
thf(5866,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v2_t_0topsp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(801,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_tsep_1) ).
thf(5521,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(946,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ) ),
inference(cnf,[status(esa)],[945]) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[946]) ).
thf(6844,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,948]) ).
thf(6845,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6844]) ).
thf(6846,plain,
! [A: $i] :
( ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ ( A @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(pattern_uni,[status(thm)],[6845:[bind(A,$thf( sk1 ))]]) ).
thf(6905,plain,
! [A: $i] :
( ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ ( A @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6846]) ).
thf(30642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( C @ ( D @ k2_xboole_0 ) ) )
| ( ( C @ ( A @ ( B @ k2_xboole_0 ) @ k3_xboole_0 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3473,21729]) ).
thf(30643,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ k2_xboole_0 ) @ k3_xboole_0 ) )
= B ),
inference(pattern_uni,[status(thm)],[30642:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k6_pre_topc ) )
= B )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
thf(2552,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k6_pre_topc ) )
= B )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(12318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( C @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3296,3332]) ).
thf(12319,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[12318:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(845,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ v2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_pre_topc) ).
thf(5802,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ v2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tops_1) ).
thf(1115,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(340,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tex_2) ).
thf(2929,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) ) ) )
=> ( A @ ( B @ v2_tex_2 ) ) )
& ( ( A @ ( B @ v2_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(827,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tsp_2) ).
thf(5727,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(542,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v3_tdlat_3 )
& ~ ( A @ v2_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_tsp_1) ).
thf(3835,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v3_tdlat_3 )
& ~ ( A @ v2_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(3708,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(2982,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(2983,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(miniscope,[status(thm)],[2982]) ).
thf(2984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ r1_tarski ) )
| ~ ( D @ ( C @ r1_tarski ) ) )
& ( ( A @ ( B @ r1_tarski ) )
| ( A != B ) )
& ( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[2983]) ).
thf(2985,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[2984]) ).
thf(2988,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[2985]) ).
thf(2989,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[2988]) ).
thf(72,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_tex_2) ).
thf(1362,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(640,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc40_tex_2) ).
thf(4507,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(625,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_tex_3) ).
thf(4400,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(260,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_tex_4 ) @ ( B @ ( A @ k6_tex_4 ) @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_tex_4) ).
thf(2456,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_tex_4 ) @ ( B @ ( A @ k6_tex_4 ) @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(871,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v1_tsep_1 ) )
| ( A @ ( B @ v1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v2_t_0topsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tsp_1) ).
thf(5888,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v1_tsep_1 ) )
| ( A @ ( B @ v1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v2_t_0topsp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(651,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tsep_1) ).
thf(4600,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(258,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k5_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_tex_4) ).
thf(2451,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k5_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_tops_1) ).
thf(1136,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k20_borsuk_1) ).
thf(3525,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(671,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_tex_3) ).
thf(4724,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
& ( B != C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_tsp_1) ).
thf(1020,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
& ( B != C ) ) ) )
=> ( A @ v2_t_0topsp ) )
& ( ( A @ v2_t_0topsp )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
& ( B != C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(1051,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(852,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k4_tdlat_1 )
= ( A @ k8_tdlat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_tdlat_3) ).
thf(5834,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k4_tdlat_1 )
= ( A @ k8_tdlat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(5787,plain,
sk329 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5784]) ).
thf(212,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tdlat_3) ).
thf(2222,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) ) ) ) )
=> ( A @ v4_tdlat_3 ) )
& ( ( A @ v4_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(666,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_tsep_1 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_tsep_1) ).
thf(4696,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_tsep_1 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(214,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( B @ ( D @ v4_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_tops_3) ).
thf(2237,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( B @ ( D @ v4_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1415,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1414]) ).
thf(757,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_borsuk_1 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc30_tex_2) ).
thf(5264,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_borsuk_1 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(6002,plain,
sk338 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[6001]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(3322,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(872,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tsp_2 ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tsp_2) ).
thf(5892,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tsp_2 ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(310,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ ( B @ v4_tex_2 ) )
& ( ( A @ ( B @ v4_pre_topc ) )
| ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_tex_2) ).
thf(2794,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ ( B @ v4_tex_2 ) )
& ( ( A @ ( B @ v4_pre_topc ) )
| ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(649,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_tex_3) ).
thf(4583,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(127,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tex_2 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_tex_2) ).
thf(1714,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tex_2 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(628,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_tex_3) ).
thf(4443,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(369,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v5_tex_2 ) ) ) )
& ( A @ ( B @ v4_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_tex_2) ).
thf(3075,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v5_tex_2 ) ) ) )
& ( A @ ( B @ v4_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_subset_1) ).
thf(1450,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( A @ ( C @ v3_pre_topc ) )
<=> ( B @ ( D @ v3_pre_topc ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_tops_3) ).
thf(2090,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( B @ ( D @ v3_pre_topc ) )
=> ( A @ ( C @ v3_pre_topc ) ) )
& ( ( A @ ( C @ v3_pre_topc ) )
=> ( B @ ( D @ v3_pre_topc ) ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(443,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_borsuk_1) ).
thf(3393,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(350,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(2994,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(2995,plain,
! [A: $i] :
( ( A @ sk179 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[2994]) ).
thf(2996,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) ),
inference(cnfConj,[status(thm)],[2995]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(3724,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_tops_1) ).
thf(1040,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2891,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(2892,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[2891]) ).
thf(2893,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[2892]) ).
thf(116,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_pre_topc) ).
thf(1632,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(3670,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(218,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v3_tex_4 ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tsp_2) ).
thf(2259,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v3_tex_4 ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v3_tex_4 ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(567,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) ) )
<=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_tex_3) ).
thf(4001,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) ) ) )
& ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(3725,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[3724]) ).
thf(3726,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[3725]) ).
thf(21688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( ( A @ ( B @ k3_xboole_0 ) @ ( C @ k2_xboole_0 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3296,3726]) ).
thf(21689,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(pattern_uni,[status(thm)],[21688:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(25621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ( A
= ( C @ ( D @ k2_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21689,3473]) ).
thf(25622,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= B ),
inference(pattern_uni,[status(thm)],[25621:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ k3_xboole_0 ) ))]]) ).
thf(25710,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= B ),
inference(simp,[status(thm)],[25622]) ).
thf(40741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( ( D @ ( A @ ( B @ k3_xboole_0 ) @ k2_xboole_0 ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[3296,25710]) ).
thf(40742,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ k3_xboole_0 ) @ k2_xboole_0 ) )
= B ),
inference(pattern_uni,[status(thm)],[40741:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(767,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc35_tex_2) ).
thf(5333,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(3163,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tops_1) ).
thf(1828,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ m1_eqrel_1 ) )
& ~ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_borsuk_1) ).
thf(2925,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ m1_eqrel_1 ) )
& ~ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_borsuk_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_borsuk_1) ).
thf(5804,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_borsuk_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(741,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
<=> ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tsep_1) ).
thf(5156,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_xboole_0 ) )
=> ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_3) ).
thf(937,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(486,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tex_2) ).
thf(3569,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(1552,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1553,plain,
( ~ ? [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ? [A: $i,B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[1552]) ).
thf(1554,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( D @ ( C @ k3_xboole_0 ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ ( B @ sk61 ) @ r2_hidden ) )
| ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1553]) ).
thf(1556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1554]) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[1556]) ).
thf(30826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( A @ ( E @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3200,1557]) ).
thf(30827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ k2_xboole_0 ) @ ( B @ r1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30826:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ k2_xboole_0 ) ))]]) ).
thf(30853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ k2_xboole_0 ) @ ( B @ r1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30827]) ).
thf(5985,plain,
sk337 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5984]) ).
thf(693,axiom,
( ( k22_borsuk_1 @ v2_pre_topc )
& ( k22_borsuk_1 @ v1_pre_topc )
& ~ ( k22_borsuk_1 @ v3_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_borsuk_1) ).
thf(4871,plain,
( ( k22_borsuk_1 @ v2_pre_topc )
& ( k22_borsuk_1 @ v1_pre_topc )
& ~ ( k22_borsuk_1 @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(1960,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(3300,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(5761,plain,
sk327 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5758]) ).
thf(664,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc49_tex_2) ).
thf(4686,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(773,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5360,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(389,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ k1_tex_2 ) @ v2_tex_2 ) )
<=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ v1_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_tex_2) ).
thf(3152,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ v1_tex_2 ) )
=> ( A @ ( B @ ( A @ k1_tex_2 ) @ v2_tex_2 ) ) )
& ( ( A @ ( B @ ( A @ k1_tex_2 ) @ v2_tex_2 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ v1_tex_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[973]) ).
thf(751,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tex_4) ).
thf(5220,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ( ( A @ ( B @ sk5 ) )
!= ( A @ ( B @ sk6 ) ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(988,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) ) ),
inference(lifteq,[status(thm)],[964]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ v1_tex_2 ) )
& ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) )
& ~ ( B @ ( A @ k1_tops_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_tex_4) ).
thf(2750,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ v1_tex_2 ) )
& ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) )
& ~ ( B @ ( A @ k1_tops_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(546,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_tex_4) ).
thf(3870,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k6_tex_4 ) @ m1_pre_topc ) )
& ( B @ ( A @ k6_tex_4 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_tex_4) ).
thf(2392,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k6_tex_4 ) @ m1_pre_topc ) )
& ( B @ ( A @ k6_tex_4 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(8740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( B @ ( C @ r1_tarski ) ) )
| ~ $true
| ~ ( C @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[2989,1227]) ).
thf(8741,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( B @ ( C @ r1_tarski ) ) )
| ~ ( C @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[8740]) ).
thf(8742,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[8741:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(565,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc36_tex_2) ).
thf(3986,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(882,axiom,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(5927,plain,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(5928,plain,
( ( sk334 @ v2_pre_topc )
& ( sk334 @ v1_pre_topc )
& ~ ( sk334 @ v3_struct_0 )
& ( sk334 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5927]) ).
thf(5929,plain,
sk334 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5928]) ).
thf(239,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_tops_3) ).
thf(2367,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_partfun1) ).
thf(3068,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(596,axiom,
? [A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_tdlat_3) ).
thf(4227,plain,
? [A: $i] :
( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(4228,plain,
( ( sk239 @ v3_tdlat_3 )
& ( sk239 @ v2_pre_topc )
& ( sk239 @ v1_pre_topc )
& ( sk239 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[4227]) ).
thf(4230,plain,
sk239 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[4228]) ).
thf(780,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ( A @ v5_tdlat_3 )
& ( A @ v4_tdlat_3 )
& ( A @ v3_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_tsp_1) ).
thf(5401,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ( A @ v5_tdlat_3 )
& ( A @ v4_tdlat_3 )
& ( A @ v3_tdlat_3 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(399,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( A @ ( D @ v3_tops_1 ) )
& ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( B @ ( E @ v3_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_tops_3) ).
thf(3189,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( A @ ( D @ v3_tops_1 ) )
& ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( B @ ( E @ v3_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(3104,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[3103]) ).
thf(57928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( E @ r1_tarski ) ) )
| ~ $true
| ~ ( E @ ( D @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3104,1227]) ).
thf(57929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( E @ r1_tarski ) ) )
| ~ ( E @ ( D @ r2_hidden ) ) ),
inference(simp,[status(thm)],[57928]) ).
thf(57930,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[57929:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( I @ ( H @ k2_xboole_0 ) )),bind(E,$thf( G @ ( H @ k3_xboole_0 ) ))]]) ).
thf(58083,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ),
inference(simp,[status(thm)],[57930]) ).
thf(777,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
=> ( ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_tdlat_3) ).
thf(5384,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
=> ( ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(732,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v2_tdlat_3 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_tex_4) ).
thf(5101,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v2_tdlat_3 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(837,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset )
= ( A @ a_1_0_lopclset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lopclset) ).
thf(5772,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset )
= ( A @ a_1_0_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(142,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_tops_3) ).
thf(1796,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(78,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_tdlat_3) ).
thf(1394,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) ) ) ) )
=> ( A @ v4_tdlat_3 ) )
& ( ( A @ v4_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(762,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( A @ r3_tsep_1 ) ) )
=> ( ( ( D @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) )
& ( B @ ( D @ ( A @ k2_tsep_1 ) ) @ ( B @ ( C @ ( A @ k2_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) ) )
| ( B @ ( D @ ( A @ r1_tsep_1 ) ) )
| ( B @ ( C @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_tsep_1) ).
thf(5296,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( A @ r3_tsep_1 ) ) )
=> ( ( ( D @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) )
& ( B @ ( D @ ( A @ k2_tsep_1 ) ) @ ( B @ ( C @ ( A @ k2_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) ) )
| ( B @ ( D @ ( A @ r1_tsep_1 ) ) )
| ( B @ ( C @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(13,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_tex_4 ) @ ( B @ ( A @ k1_tex_2 ) @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_tex_4) ).
thf(998,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_tex_4 ) @ ( B @ ( A @ k1_tex_2 ) @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_pre_topc )
& ~ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tsep_1) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_pre_topc )
& ~ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k1_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_tops_1) ).
thf(2809,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k1_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(163,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_tex_4) ).
thf(1943,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(1201,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ v2_tops_1 ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ ( B @ v2_tops_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc ) ),
inference(cnf,[status(esa)],[937]) ).
thf(6263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ( A @ ( C @ v2_tops_1 ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ ( B @ v2_tops_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[919,938]) ).
thf(6264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ( A @ ( C @ v2_tops_1 ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ ( B @ v2_tops_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[6263]) ).
thf(6265,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ v2_tops_1 ) )
| ~ ( A @ ( B @ r1_tarski ) )
| ~ ( sk1 @ ( A @ v2_tops_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[6264:[bind(A,$thf( sk1 ))]]) ).
thf(6315,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ v2_tops_1 ) )
| ~ ( A @ ( B @ r1_tarski ) )
| ~ ( sk1 @ ( A @ v2_tops_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(simp,[status(thm)],[6265]) ).
thf(6326,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ v2_tops_1 ) )
| ~ ( A @ ( B @ r1_tarski ) )
| ~ ( sk1 @ ( A @ v2_tops_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6315,922]) ).
thf(6327,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ v2_tops_1 ) )
| ~ ( A @ ( B @ r1_tarski ) )
| ~ ( sk1 @ ( A @ v2_tops_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6326]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2965,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(817,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_tex_3) ).
thf(5665,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(3588,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) @ ( B @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( B @ r2_hidden ) )
& ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_tops_1) ).
thf(1242,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ r2_hidden ) )
& ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k1_tops_1 ) @ ( B @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( B @ r2_hidden ) )
& ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(484,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ v3_tops_1 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_tops_3) ).
thf(3559,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ v3_tops_1 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(849,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k3_tdlat_1 )
= ( A @ k7_tdlat_1 ) )
& ( ( A @ k2_tdlat_1 )
= ( A @ k6_tdlat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_tdlat_3) ).
thf(5819,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k3_tdlat_1 )
= ( A @ k7_tdlat_1 ) )
& ( ( A @ k2_tdlat_1 )
= ( A @ k6_tdlat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(473,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( A @ ( B @ m1_pre_topc ) )
<=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_pre_topc @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) )
& ( A @ k2_pre_topc @ ( B @ k2_pre_topc @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_pre_topc) ).
thf(3492,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ u1_pre_topc @ ( C @ r2_hidden ) ) )
& ( ( B @ u1_pre_topc @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ k2_pre_topc @ ( B @ k2_pre_topc @ r1_tarski ) ) )
=> ( A @ ( B @ m1_pre_topc ) ) )
& ( ( A @ ( B @ m1_pre_topc ) )
=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ u1_pre_topc @ ( C @ r2_hidden ) ) )
& ( ( B @ u1_pre_topc @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ k2_pre_topc @ ( B @ k2_pre_topc @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(447,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( C @ v1_tsp_2 ) )
<=> ( A @ ( B @ v2_tsp_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tsp_2) ).
thf(3406,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
=> ( A @ ( C @ v1_tsp_2 ) ) )
& ( ( A @ ( C @ v1_tsp_2 ) )
=> ( A @ ( B @ v2_tsp_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(397,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( D @ ( B @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_tops_3) ).
thf(3184,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( D @ ( B @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(667,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( ( A @ ( C @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) ) )
| ( ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( B @ v4_tex_3 ) ) ) )
=> ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v3_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_tex_3) ).
thf(4700,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( ( A @ ( C @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) ) )
| ( ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( B @ v4_tex_3 ) ) ) )
=> ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v3_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(2922,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(891,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_pre_topc ) )
=> ( A @ ( C @ m1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tsep_1) ).
thf(5961,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_pre_topc ) )
=> ( A @ ( C @ m1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(408,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ k4_t_0topsp @ k2_relat_1 @ r1_tarski ) )
& ( ( A @ k4_t_0topsp @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_t_0topsp) ).
thf(3229,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ k4_t_0topsp @ k2_relat_1 @ r1_tarski ) )
& ( ( A @ k4_t_0topsp @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(920,plain,
~ ( sk2 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[917]) ).
thf(460,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( D @ ( B @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_3) ).
thf(3450,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( D @ ( B @ k6_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(5751,plain,
~ ( sk326 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5749]) ).
thf(718,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_tex_3) ).
thf(5017,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(3186,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(190,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
| ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_tex_2) ).
thf(2118,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
| ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v1_tsp_1 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tsp_2) ).
thf(1338,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v1_tsp_1 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) )
=> ( A @ ( B @ v1_tsp_2 ) ) )
& ( ( A @ ( B @ v1_tsp_2 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v1_tsp_1 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(173,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(2047,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(701,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v2_t_0topsp )
& ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_tsp_1) ).
thf(4925,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v2_t_0topsp )
& ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(510,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C @ ( D @ r1_tarski ) ) )
=> ( B @ ( D @ v2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_tops_3) ).
thf(3679,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C @ ( D @ r1_tarski ) ) )
=> ( B @ ( D @ v2_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(4216,plain,
sk238 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[4215]) ).
thf(492,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_tex_3) ).
thf(3591,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(336,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
<=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tex_3) ).
thf(2910,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
=> ( A @ ( B @ v3_tex_3 ) ) )
& ( ( A @ ( B @ v3_tex_3 ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(208,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_tdlat_3) ).
thf(2204,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) )
=> ( A @ v3_tdlat_3 ) )
& ( ( A @ v3_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( A @ ( C @ v6_compts_1 ) )
<=> ( B @ ( D @ v6_compts_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_borsuk_1) ).
thf(3303,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( B @ ( D @ v6_compts_1 ) )
=> ( A @ ( C @ v6_compts_1 ) ) )
& ( ( A @ ( C @ v6_compts_1 ) )
=> ( B @ ( D @ v6_compts_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k21_borsuk_1 ) ) )
= ( C @ ( B @ k16_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k21_borsuk_1) ).
thf(4962,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k21_borsuk_1 ) ) )
= ( C @ ( B @ k16_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(909,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m1_tsp_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_tsp_1) ).
thf(6015,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m1_tsp_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k7_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k7_tex_4 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc19_tex_4) ).
thf(2574,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k7_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k7_tex_4 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(394,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tex_3) ).
thf(3169,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) )
=> ( A @ ( B @ v3_tex_3 ) ) )
& ( ( A @ ( B @ v3_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v2_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(15271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ( ( A @ ( B @ k2_xboole_0 ) @ ( C @ k3_xboole_0 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3473,3200]) ).
thf(15272,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(pattern_uni,[status(thm)],[15271:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(30824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( A @ ( E @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[15272,1557]) ).
thf(30825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ k2_xboole_0 ) @ ( C @ r1_xboole_0 ) )
| ~ ( C @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30824:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ k2_xboole_0 ) ))]]) ).
thf(30852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ k2_xboole_0 ) @ ( C @ r1_xboole_0 ) )
| ~ ( C @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30825]) ).
thf(635,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_tsep_1) ).
thf(4480,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(925,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(804,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) ) )
<=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_tex_3) ).
thf(5545,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) ) ) )
& ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(727,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc42_tex_2) ).
thf(5070,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(782,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_tdlat_3) ).
thf(5416,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(296,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
<=> ( ( C @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( C @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_tex_4) ).
thf(2737,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( C @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
& ( ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( C @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(530,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_tex_3) ).
thf(3767,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_4 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v1_tex_4 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v1_tex_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_tex_4) ).
thf(2296,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v1_tex_4 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v1_tex_4 ) ) )
=> ( A @ ( B @ v3_tex_4 ) ) )
& ( ( A @ ( B @ v3_tex_4 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v1_tex_4 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v1_tex_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(2621,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(309,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
| ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_tops_3) ).
thf(2790,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
| ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(760,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( C @ ( B @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_topmetr) ).
thf(5281,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( C @ ( B @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(118,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
<=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tdlat_3) ).
thf(1636,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) )
& ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(2441,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(633,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tsp_1) ).
thf(4466,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(278,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ k2_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_tops_1) ).
thf(2596,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ k2_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) )
& ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(1255,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) )
& ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
<=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tops_3) ).
thf(1123,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( A @ u1_struct_0 ) )
=> ( A @ ( B @ v1_tops_3 ) ) )
& ( ( A @ ( B @ v1_tops_3 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(593,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc31_tex_3) ).
thf(4204,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(639,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_tex_3) ).
thf(4499,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(532,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_tdlat_3) ).
thf(3778,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(3261,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(12316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( C @ ( A @ ( B @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3296,3332]) ).
thf(12317,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ k3_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[12316:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(12384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( C @ ( D @ k3_xboole_0 ) ) )
| ( C @ ( A @ ( B @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3296,12317]) ).
thf(12385,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ k3_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[12384:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(669,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( ( ~ ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( B @ ( A @ r1_tsep_1 ) ) )
& ~ ( D @ ( C @ ( A @ r1_tsep_1 ) ) ) )
| ( ~ ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
& ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( B @ ( A @ k2_tsep_1 ) ) ) ) )
& ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( B @ ( C @ ( A @ k2_tsep_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tsep_1) ).
thf(4712,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( ( ~ ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( B @ ( A @ r1_tsep_1 ) ) )
& ~ ( D @ ( C @ ( A @ r1_tsep_1 ) ) ) )
| ( ~ ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
& ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( B @ ( A @ k2_tsep_1 ) ) ) ) )
& ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( B @ ( C @ ( A @ k2_tsep_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(2601,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(540,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tex_4) ).
thf(3827,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ ( A @ k6_tex_4 ) @ v2_tex_2 ) )
& ( B @ ( A @ k6_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_tex_4 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc18_tex_4) ).
thf(3711,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ ( A @ k6_tex_4 ) @ v2_tex_2 ) )
& ( B @ ( A @ k6_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_tex_4 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = B )
=> ( C @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_tops_2) ).
thf(2560,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = B )
=> ( C @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(561,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_tex_2) ).
thf(3972,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(497,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( A @ ( B @ m1_tsp_1 ) )
<=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ v3_pre_topc ) )
<=> ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tsp_1) ).
thf(3603,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( C @ v3_pre_topc ) )
=> ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
=> ( A @ ( B @ m1_tsp_1 ) ) )
& ( ( A @ ( B @ m1_tsp_1 ) )
=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( C @ v3_pre_topc ) )
=> ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tsep_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tsep_1) ).
thf(1042,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v3_pre_topc ) ) ) )
=> ( A @ ( B @ v1_tsep_1 ) ) )
& ( ( A @ ( B @ v1_tsep_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(950,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ k1_tops_1 ) )
= ( E @ ( B @ k1_tops_1 ) ) )
| ( D != E )
| ~ ( C @ ( D @ r1_tarski ) )
| ~ ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ m1_pre_topc ) )
| ( B @ v3_struct_0 )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[949]) ).
thf(951,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ r1_tarski ) )
| ~ ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ m1_pre_topc ) )
| ( B @ v3_struct_0 )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 )
| ( ( D @ ( A @ k1_tops_1 ) )
= ( E @ ( B @ k1_tops_1 ) ) )
| ( D != E ) ),
inference(lifteq,[status(thm)],[950]) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ r1_tarski ) )
| ~ ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ m1_pre_topc ) )
| ( B @ v3_struct_0 )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 )
| ( ( D @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ),
inference(simp,[status(thm)],[951]) ).
thf(104,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_tex_2) ).
thf(1570,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(41,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tdlat_3) ).
thf(1174,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v3_pre_topc ) ) ) )
=> ( A @ v4_tdlat_3 ) )
& ( ( A @ v4_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v3_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(601,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc22_tex_3) ).
thf(4252,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(889,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( B @ ( A @ k1_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_tsep_1) ).
thf(5956,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( B @ ( A @ k1_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(4521,plain,
sk255 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[4520]) ).
thf(21636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ( A
= ( C @ ( D @ k2_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3726,3473]) ).
thf(21637,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(pattern_uni,[status(thm)],[21636:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ k3_xboole_0 ) ))]]) ).
thf(21695,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(simp,[status(thm)],[21637]) ).
thf(30576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( ( C @ ( A @ ( B @ k3_xboole_0 ) @ k2_xboole_0 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3296,21695]) ).
thf(30577,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(pattern_uni,[status(thm)],[30576:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(147,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_3) ).
thf(1824,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(5754,plain,
sk326 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5749]) ).
thf(170,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tdlat_3) ).
thf(2032,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(3054,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[3053]) ).
thf(3055,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[3054]) ).
thf(30810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k3_xboole_0 ) )
!= ( C @ ( B @ k3_xboole_0 ) ) )
| ~ ( C @ ( B @ r1_xboole_0 ) )
| ~ ( A @ ( D @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3055,1557]) ).
thf(30811,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ r1_xboole_0 ) )
| ~ ( A @ ( B @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30810:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(30847,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ r1_xboole_0 ) )
| ~ ( A @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30811]) ).
thf(538,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_tsp_1) ).
thf(3814,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(246,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ v2_compts_1 ) )
=> ( A @ ( B @ v6_compts_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_compts_1) ).
thf(2396,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ v2_compts_1 ) )
=> ( A @ ( B @ v6_compts_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(3682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(102,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tex_2 ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_tex_2) ).
thf(1560,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tex_2 ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(558,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_3) ).
thf(3948,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_tops_1) ).
thf(2433,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(7327,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ $true
| ~ ( A @ l1_pre_topc ) ),
inference(paramod_ordered,[status(thm)],[918,956]) ).
thf(7328,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[7327]) ).
thf(7329,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk2 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[7328:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(7502,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk2 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7329,922]) ).
thf(7503,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk2 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[7502]) ).
thf(626,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
<=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_tsep_1) ).
thf(4402,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(712,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
& ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc45_tex_2) ).
thf(4979,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
& ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(210,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( C @ ( B @ r1_tarski ) )
& ~ ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tex_4) ).
thf(2213,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( C @ ( B @ r1_tarski ) )
& ~ ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( C @ ( B @ r1_tarski ) )
& ~ ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(2345,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v4_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tdlat_3) ).
thf(1195,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v4_pre_topc ) ) ) )
=> ( A @ v4_tdlat_3 ) )
& ( ( A @ v4_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v4_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(3727,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(21730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[3473,12351]) ).
thf(21731,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
= B ),
inference(pattern_uni,[status(thm)],[21730:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(57990,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( E @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[21731,3104]) ).
thf(57991,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( C @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[57990:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ k2_xboole_0 ) )),bind(D,$thf( G ))]]) ).
thf(58042,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( C @ r1_tarski ) ),
inference(simp,[status(thm)],[57991]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(3166,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(564,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_tex_4) ).
thf(3980,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(152,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tdlat_3) ).
thf(1837,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(372,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_tops_3) ).
thf(3090,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_tops_1 ) )
=> ( A @ ( B @ v1_tops_3 ) ) )
& ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(9164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( D @ r1_tarski ) ) )
| ~ $true
| ~ ( D @ ( C @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3332,1227]) ).
thf(9165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( D @ r1_tarski ) ) )
| ~ ( D @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9164]) ).
thf(9166,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[9165:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ k3_xboole_0 ) ))]]) ).
thf(9181,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[9166]) ).
thf(12320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( A @ ( B @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3296,9181]) ).
thf(12321,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ k3_xboole_0 ) @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[12320:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(232,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_2 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_tex_2) ).
thf(2332,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_2 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(317,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( D @ ( B @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_tops_3) ).
thf(2826,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( D @ ( B @ k6_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
thf(2820,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(4994,plain,
sk281 @ v3_tdlat_3,
inference(cnfConj,[status(thm)],[4991]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(3297,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(8599,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2996,6483]) ).
thf(8600,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 ) ),
inference(simp,[status(thm)],[8599]) ).
thf(8702,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( A @ sk179 )
!= B )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8600]) ).
thf(8736,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( A @ sk179 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8702]) ).
thf(623,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_tsep_1) ).
thf(4385,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(164,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(1951,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(802,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v2_tdlat_3 )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tex_2) ).
thf(5534,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v2_tdlat_3 )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(3600,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( B @ ( C @ ( A @ r3_tsep_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r3_tsep_1) ).
thf(3894,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( B @ ( C @ ( A @ r3_tsep_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(839,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ l1_pre_topc )
& ( A @ k3_t_0topsp @ v2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_t_0topsp) ).
thf(5779,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ l1_pre_topc )
& ( A @ k3_t_0topsp @ v2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(117,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_tops_3) ).
thf(1634,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(77,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lopclset) ).
thf(1392,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k1_tex_2 ) @ m1_pre_topc ) )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tex_2) ).
thf(3647,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k1_tex_2 ) @ m1_pre_topc ) )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(188,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k5_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_tex_4) ).
thf(2112,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k5_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(766,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tsep_1) ).
thf(5330,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(800,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tsp_1) ).
thf(5515,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(3595,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(458,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k18_borsuk_1 ) ) )
= ( B @ ( A @ a_2_3_borsuk_1 ) @ ( C @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_borsuk_1) ).
thf(3445,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k18_borsuk_1 ) ) )
= ( B @ ( A @ a_2_3_borsuk_1 ) @ ( C @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(17,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tex_2) ).
thf(1012,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(726,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_tsep_1) ).
thf(5066,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
=> ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tsp_1) ).
thf(1402,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
=> ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(1143,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(3254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(636,axiom,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_struct_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_pcomps_1) ).
thf(4486,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_struct_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(4487,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_struct_0 )
= A ),
inference(cnf,[status(esa)],[4486]) ).
thf(4488,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_struct_0 )
= A ),
inference(lifteq,[status(thm)],[4487]) ).
thf(8226,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[4488,7503]) ).
thf(8282,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 )
!= sk2 )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[8226]) ).
thf(573,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc50_tex_2) ).
thf(4048,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(4525,plain,
sk255 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[4520]) ).
thf(597,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_3) ).
thf(4233,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) )
=> ( A @ ( B @ v2_tex_3 ) ) )
& ( ( A @ ( B @ v2_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(5361,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5360]) ).
thf(5362,plain,
~ ( sk298 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5361]) ).
thf(286,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
thf(2631,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(4219,plain,
sk238 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[4215]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k4_tsp_2 ) )
= ( B @ ( A @ k1_tsp_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_tsp_2) ).
thf(5854,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k4_tsp_2 ) )
= ( B @ ( A @ k1_tsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(162,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_tops_1) ).
thf(1936,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(586,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc14_tex_2) ).
thf(4123,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_tops_1) ).
thf(1360,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(748,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B @ ( C @ m1_pre_topc ) )
& ( D @ ( C @ ( A @ r3_tsep_2 ) ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v3_tex_3 ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ( D @ v1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_tex_3) ).
thf(5189,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B @ ( C @ m1_pre_topc ) )
& ( D @ ( C @ ( A @ r3_tsep_2 ) ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v3_tex_3 ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ( D @ v1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(375,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_tops_3) ).
thf(3105,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(812,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc15_tex_2) ).
thf(5626,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(553,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_tdlat_3) ).
thf(3909,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(875,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) ) )
=> ( A @ ( C @ v4_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_tex_3) ).
thf(5904,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) ) )
=> ( A @ ( C @ v4_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_tops_1) ).
thf(1259,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3122,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(342,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) ) )
=> ( ( ( B @ ( E @ v1_tops_1 ) )
& ( A @ ( C @ v1_tops_1 ) ) )
<=> ( A @ ( D @ v1_tops_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_tops_3) ).
thf(2946,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) ) )
=> ( ( ( A @ ( D @ v1_tops_1 ) )
=> ( ( B @ ( E @ v1_tops_1 ) )
& ( A @ ( C @ v1_tops_1 ) ) ) )
& ( ( ( B @ ( E @ v1_tops_1 ) )
& ( A @ ( C @ v1_tops_1 ) ) )
=> ( A @ ( D @ v1_tops_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(753,axiom,
? [A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pre_topc) ).
thf(5238,plain,
? [A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(5673,plain,
~ ( sk320 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5672]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_subset_1) ).
thf(1121,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(844,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tsp_2) ).
thf(5798,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[977]) ).
thf(4636,plain,
sk264 @ v2_t_0topsp,
inference(cnfConj,[status(thm)],[4632]) ).
thf(331,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(2887,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(2888,plain,
! [A: $i] : ( A @ ( A @ sk174 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[2887]) ).
thf(8061,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk174 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2888,6483]) ).
thf(8062,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk174 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 ) ),
inference(simp,[status(thm)],[8061]) ).
thf(8063,plain,
( ( sk1 @ ( sk1 @ u1_struct_0 @ sk174 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 ) ),
inference(pattern_uni,[status(thm)],[8062:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( sk1 @ u1_struct_0 @ sk174 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v1_tex_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tex_4) ).
thf(1138,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v1_tex_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(702,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v4_tex_3 ) ) ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_tex_3) ).
thf(4930,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v4_tex_3 ) ) ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(887,axiom,
? [A: $i] : ( A @ l1_pre_topc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(5951,plain,
? [A: $i] : ( A @ l1_pre_topc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[968]) ).
thf(371,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C @ ( D @ r1_tarski ) ) )
=> ( B @ ( D @ v3_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_tops_3) ).
thf(3087,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C @ ( D @ r1_tarski ) ) )
=> ( B @ ( D @ v3_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(698,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v1_tex_3 ) )
| ( A @ ( B @ v1_tex_3 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_tex_3) ).
thf(4898,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v1_tex_3 ) )
| ( A @ ( B @ v1_tex_3 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(30830,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( B @ ( A @ k3_xboole_0 ) @ ( E @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3296,1557]) ).
thf(30831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ r1_xboole_0 ) )
| ~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30830:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(30855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ r1_xboole_0 ) )
| ~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30831]) ).
thf(662,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tex_4) ).
thf(4676,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(311,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( A @ u1_struct_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_tops_3) ).
thf(2798,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( A @ u1_struct_0 ) ) ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( A @ u1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(5830,plain,
sk330 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5828]) ).
thf(744,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_tex_2) ).
thf(5166,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(386,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_tops_3) ).
thf(3143,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(8103,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk174 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ~ $true
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(paramod_ordered,[status(thm)],[2888,6486]) ).
thf(8104,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk174 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8103]) ).
thf(8105,plain,
( ( sk329 != sk1 )
| ( sk1 @ ( sk1 @ u1_struct_0 @ sk174 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(pattern_uni,[status(thm)],[8104:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( sk1 @ u1_struct_0 @ sk174 ))]]) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( C @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[932]) ).
thf(5743,plain,
sk324 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5738]) ).
thf(8344,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( sk329 != sk1 )
| ( sk1 @ ( A @ sk174 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(paramod_ordered,[status(thm)],[4488,8105]) ).
thf(8346,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 )
!= sk1 )
| ( sk329 != sk1 )
| ( sk1 @ ( A @ sk174 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8344]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(1644,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(425,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(3311,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_3_borsuk_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ~ ( C @ u1_struct_0 @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k1_struct_0 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_borsuk_1) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ~ ( C @ u1_struct_0 @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k1_struct_0 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_borsuk_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_borsuk_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ~ ( C @ u1_struct_0 @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k1_struct_0 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( B @ ( C @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_tops_1) ).
thf(2830,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( B @ ( C @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(734,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( C
= ( B @ ( A @ k16_borsuk_1 ) ) )
<=> ( ( ( C @ u1_pre_topc )
= ( B @ ( A @ a_2_2_borsuk_1 ) ) )
& ( ( C @ u1_struct_0 )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_borsuk_1) ).
thf(5107,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( ( ( ( C @ u1_pre_topc )
= ( B @ ( A @ a_2_2_borsuk_1 ) ) )
& ( ( C @ u1_struct_0 )
= B ) )
=> ( C
= ( B @ ( A @ k16_borsuk_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k16_borsuk_1 ) ) )
=> ( ( ( C @ u1_pre_topc )
= ( B @ ( A @ a_2_2_borsuk_1 ) ) )
& ( ( C @ u1_struct_0 )
= B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(30780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ k2_xboole_0 ) @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( A @ ( E @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[21729,1557]) ).
thf(30781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ k2_xboole_0 ) @ r1_xboole_0 ) )
| ~ ( C @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30780:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ k2_xboole_0 ) )),bind(D,$thf( G ))]]) ).
thf(30860,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ k2_xboole_0 ) @ r1_xboole_0 ) )
| ~ ( C @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30781]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ k2_pre_topc @ ( C @ r1_tarski ) )
=> ( ( A @ ( C @ v6_compts_1 ) )
<=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = C )
=> ( B @ ( D @ v6_compts_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_compts_1) ).
thf(3094,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ k2_pre_topc @ ( C @ r1_tarski ) )
=> ( ( ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = C )
=> ( B @ ( D @ v6_compts_1 ) ) ) )
=> ( A @ ( C @ v6_compts_1 ) ) )
& ( ( A @ ( C @ v6_compts_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = C )
=> ( B @ ( D @ v6_compts_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(89,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ r1_tarski ) ) )
=> ( C
= ( A @ u1_struct_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_3) ).
thf(1461,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ r1_tarski ) ) )
=> ( C
= ( A @ u1_struct_0 ) ) ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ r1_tarski ) ) )
=> ( C
= ( A @ u1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tsep_1) ).
thf(3441,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(3010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(791,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_4) ).
thf(5464,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(5786,plain,
~ ( sk329 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5784]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(2080,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(5253,plain,
~ ( sk290 @ v1_tdlat_3 ),
inference(cnfConj,[status(thm)],[5248]) ).
thf(205,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v6_compts_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_borsuk_1) ).
thf(2196,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v6_compts_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(674,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
<=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_tsep_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( F @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ~ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) ) )
& ( C @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_tsep_1) ).
thf(4744,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_tsep_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( F @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ~ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) ) )
& ( C @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_tsep_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( F @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ~ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) ) )
& ( C @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tex_2 ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v3_tex_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_tex_2) ).
thf(2613,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tex_2 ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v3_tex_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(5932,plain,
sk334 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5928]) ).
thf(6759,plain,
( ( ( sk337 @ v2_t_0topsp )
!= ( sk238 @ v2_t_0topsp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5988,4220]) ).
thf(6760,plain,
( ( sk337 @ v2_t_0topsp )
!= ( sk238 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[6759]) ).
thf(6763,plain,
sk337 != sk238,
inference(simp,[status(thm)],[6760]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tex_2 ) )
| ( A @ ( B @ v3_tex_2 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_tex_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tex_2) ).
thf(2172,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tex_2 ) )
| ( A @ ( B @ v3_tex_2 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_tex_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(658,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc32_tex_3) ).
thf(4648,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g1_pre_topc ) @ l1_pre_topc )
& ( B @ ( A @ g1_pre_topc ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(3428,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g1_pre_topc ) @ l1_pre_topc )
& ( B @ ( A @ g1_pre_topc ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(816,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ ( C @ m1_pre_topc ) )
& ( C @ ( B @ m1_pre_topc ) ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tsep_1) ).
thf(5662,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ ( C @ m1_pre_topc ) )
& ( C @ ( B @ m1_pre_topc ) ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tex_2 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v3_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_tex_2) ).
thf(2349,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tex_2 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v3_tex_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_pre_topc) ).
thf(1612,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(348,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
<=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tex_3) ).
thf(2978,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
=> ( A @ ( B @ v1_tops_3 ) ) )
& ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(306,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_tops_3) ).
thf(2781,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(644,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) )
=> ( ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
<=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_borsuk_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( F @ m1_pre_topc ) )
& ( A
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ( A
!= ( E @ ( D @ ( A @ k1_tsep_1 ) ) ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_tsep_1) ).
thf(4530,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) )
=> ( ( ( ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_borsuk_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( F @ m1_pre_topc ) )
& ( A
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ( A
!= ( E @ ( D @ ( A @ k1_tsep_1 ) ) ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_borsuk_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( F @ m1_pre_topc ) )
& ( A
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ( A
!= ( E @ ( D @ ( A @ k1_tsep_1 ) ) ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(410,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ~ ( B @ v1_xboole_0 )
<=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tex_3) ).
thf(3242,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) )
=> ~ ( B @ v1_xboole_0 ) )
& ( ~ ( B @ v1_xboole_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(516,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tex_2) ).
thf(3701,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(3702,plain,
! [A: $i] :
( ( ~ ( A @ k1_zfmisc_1 @ ( A @ sk214 @ v1_tex_2 ) )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk214 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk214 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3701]) ).
thf(3703,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ sk214 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3702]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D
= ( B @ u1_struct_0 @ ( C @ k3_xboole_0 ) ) )
& ( B @ ( D @ v3_pre_topc ) ) ) )
& ( A @ ( C @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tsp_1) ).
thf(1249,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D
= ( B @ u1_struct_0 @ ( C @ k3_xboole_0 ) ) )
& ( B @ ( D @ v3_pre_topc ) ) ) )
& ( A @ ( C @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(481,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_tdlat_3 )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_tex_2) ).
thf(3541,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_tdlat_3 )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(776,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_tex_3) ).
thf(5374,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v3_compts_1 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r1_xboole_0 ) )
& ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) )
& ( B != C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_compts_1) ).
thf(1266,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r1_xboole_0 ) )
& ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) )
& ( B != C ) ) ) )
=> ( A @ v3_compts_1 ) )
& ( ( A @ v3_compts_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r1_xboole_0 ) )
& ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) )
& ( B != C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(524,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( D @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_tsep_1) ).
thf(3743,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( D @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(167,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( D @ r2_hidden ) )
& ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_tsp_1) ).
thf(1974,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( D @ r2_hidden ) )
& ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( D @ r2_hidden ) )
& ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[957]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(2566,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(4231,plain,
sk239 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[4228]) ).
thf(587,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) ) )
<=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_tex_3) ).
thf(4135,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) ) ) )
& ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(432,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( A @ ( C @ v3_tops_1 ) )
<=> ( B @ ( D @ v3_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_tops_3) ).
thf(3333,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( B @ ( D @ v3_tops_1 ) )
=> ( A @ ( C @ v3_tops_1 ) ) )
& ( ( A @ ( C @ v3_tops_1 ) )
=> ( B @ ( D @ v3_tops_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(775,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tdlat_3) ).
thf(5369,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(352,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ ( A @ k1_tex_2 ) @ u1_pre_topc @ ( C @ ( A @ k1_tex_2 ) @ u1_struct_0 @ g1_pre_topc ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_tex_2) ).
thf(3005,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ ( A @ k1_tex_2 ) @ u1_pre_topc @ ( C @ ( A @ k1_tex_2 ) @ u1_struct_0 @ g1_pre_topc ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
thf(2140,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(504,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tex_3) ).
thf(3654,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[974]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(1456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(75,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_tex_2) ).
thf(1382,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) )
& ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(322,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
| ( A @ ( B @ v3_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_3) ).
thf(2851,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
| ( A @ ( B @ v3_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(895,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_tex_2) ).
thf(5973,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(9199,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ $true
| ( sk2 @ v2_t_0topsp ) ),
inference(paramod_ordered,[status(thm)],[9190,6483]) ).
thf(9200,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk2 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[9199]) ).
thf(9201,plain,
( ( sk1 @ ( sk1 @ ( sk2 @ sk5 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk2 @ v2_t_0topsp ) ),
inference(pattern_uni,[status(thm)],[9200:[bind(A,$thf( sk1 @ ( sk2 @ sk5 ) ))]]) ).
thf(407,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ~ ( C @ v2_t_0topsp )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ~ ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_tsp_1) ).
thf(3222,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ~ ( C @ v2_t_0topsp )
& ( C @ v1_pre_topc ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ~ ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(2497,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(6005,plain,
sk338 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[6001]) ).
thf(764,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ m1_pre_topc ) )
& ( D @ ( C @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v3_tex_3 ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_tex_3) ).
thf(5305,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ m1_pre_topc ) )
& ( D @ ( C @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v3_tex_3 ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(304,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( D @ ( A @ k1_struct_0 ) ) )
& ( B @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_tex_2) ).
thf(2766,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( D @ ( A @ k1_struct_0 ) ) )
& ( B @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) )
=> ( A @ ( B @ v4_tex_2 ) ) )
& ( ( A @ ( B @ v4_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( D @ ( A @ k1_struct_0 ) ) )
& ( B @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(513,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tex_2) ).
thf(3692,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(2482,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(220,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_tex_3) ).
thf(2272,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ ( A @ k7_tex_4 ) @ v2_tex_2 ) )
& ( B @ ( A @ k7_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k7_tex_4 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc21_tex_4) ).
thf(3364,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ ( A @ k7_tex_4 ) @ v2_tex_2 ) )
& ( B @ ( A @ k7_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k7_tex_4 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(370,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tsp_1) ).
thf(3083,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ~ ( A @ v2_t_0topsp )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(403,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l19_tsp_2) ).
thf(3201,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(114,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v1_tops_1 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( B @ v1_tops_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_tops_3) ).
thf(1627,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v1_tops_1 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( B @ v1_tops_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(618,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_pre_topc) ).
thf(4361,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k6_pre_topc ) @ v1_tex_2 ) )
& ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) )
& ~ ( B @ ( A @ k6_pre_topc ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tex_4) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k6_pre_topc ) @ v1_tex_2 ) )
& ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) )
& ~ ( B @ ( A @ k6_pre_topc ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(528,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_realset2 )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_tex_2) ).
thf(3755,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_realset2 )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(5747,plain,
~ ( sk325 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5745]) ).
thf(535,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_borsuk_1 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_tsep_1) ).
thf(3802,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_borsuk_1 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(579,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_tex_3) ).
thf(4081,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_pre_topc )
& ~ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tsep_1) ).
thf(4889,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_pre_topc )
& ~ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(5833,plain,
sk330 @ v4_tdlat_3,
inference(cnfConj,[status(thm)],[5828]) ).
thf(126,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ v1_tsp_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tsp_1) ).
thf(1712,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ v1_tsp_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(6068,plain,
( ( ( sk290 @ v2_t_0topsp )
!= ( sk264 @ v2_t_0topsp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4636,5255]) ).
thf(6069,plain,
( ( sk290 @ v2_t_0topsp )
!= ( sk264 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[6068]) ).
thf(6070,plain,
sk290 != sk264,
inference(simp,[status(thm)],[6069]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_tex_3) ).
thf(1071,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(799,axiom,
? [A: $i] : ( A @ l2_quantal1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_quantal1) ).
thf(5513,plain,
? [A: $i] : ( A @ l2_quantal1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(926,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
| ~ ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[925]) ).
thf(745,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tdlat_3) ).
thf(5170,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(461,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(3454,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(391,axiom,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_pre_topc )
= ( A @ k1_pcomps_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_pcomps_1) ).
thf(3160,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_pre_topc )
= ( A @ k1_pcomps_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(3161,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_pre_topc )
= ( A @ k1_pcomps_1 ) ),
inference(cnf,[status(esa)],[3160]) ).
thf(3162,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k2_pcomps_1 @ u1_pre_topc ) ),
inference(lifteq,[status(thm)],[3161]) ).
thf(8739,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 @ u1_pre_topc )
= ( A @ k1_zfmisc_1 ) ),
inference(rewrite,[status(thm)],[3162,3197]) ).
thf(302,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v4_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_tops_1) ).
thf(2761,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(30785,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( A @ ( E @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[12351,1557]) ).
thf(30786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ k2_xboole_0 ) @ r1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30785:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ k2_xboole_0 ) )),bind(D,$thf( F ))]]) ).
thf(30837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ k2_xboole_0 ) @ r1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30786]) ).
thf(35480,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
!= ( E @ ( D @ k2_xboole_0 ) ) )
| ~ ( D @ ( A @ r1_xboole_0 ) )
| ~ ( D @ ( C @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3726,30837]) ).
thf(35481,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ r1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[35480:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ k3_xboole_0 ) ))]]) ).
thf(35515,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ r1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[35481]) ).
thf(675,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v2_tex_3 ) )
| ( A @ ( B @ v2_tex_3 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v2_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_tex_3) ).
thf(4765,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v2_tex_3 ) )
| ( A @ ( B @ v2_tex_3 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v2_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(329,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v3_tops_1 ) ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_tops_3) ).
thf(2883,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v3_tops_1 ) ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(921,plain,
~ ( sk2 @ ( sk1 @ r1_borsuk_1 ) ),
inference(cnfConj,[status(thm)],[917]) ).
thf(179,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k6_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_tex_4) ).
thf(2076,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k6_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ ( B @ v1_tsp_2 ) )
& ( ( A @ ( B @ v4_pre_topc ) )
| ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_tsp_2) ).
thf(1170,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ ( B @ v1_tsp_2 ) )
& ( ( A @ ( B @ v4_pre_topc ) )
| ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(501,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
<=> ( A @ ( C @ v3_tex_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_tex_4) ).
thf(3639,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v3_tex_4 ) )
=> ( A @ ( B @ v4_tex_4 ) ) )
& ( ( A @ ( B @ v4_tex_4 ) )
=> ( A @ ( C @ v3_tex_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(629,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_borsuk_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_tsep_1) ).
thf(4448,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_borsuk_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(947,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[946]) ).
thf(6657,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,947]) ).
thf(6658,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6657]) ).
thf(6659,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(pattern_uni,[status(thm)],[6658:[bind(A,$thf( sk1 ))]]) ).
thf(6688,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6659]) ).
thf(5930,plain,
~ ( sk334 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5928]) ).
thf(8607,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2996,6905]) ).
thf(8608,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8607]) ).
thf(8609,plain,
( ( sk1 @ ( sk1 @ u1_struct_0 @ sk179 @ v3_pre_topc ) )
| ~ ( sk1 @ ( sk1 @ u1_struct_0 @ sk179 @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
inference(pattern_uni,[status(thm)],[8608:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( sk1 @ u1_struct_0 @ sk179 ))]]) ).
thf(5249,plain,
sk290 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5248]) ).
thf(854,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v1_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tex_3) ).
thf(5840,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v1_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(864,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_tdlat_3 )
=> ( A @ v2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tdlat_3) ).
thf(5872,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_tdlat_3 )
=> ( A @ v2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(509,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(3675,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(714,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_tex_3) ).
thf(4995,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(131,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( D @ ( B @ k6_pre_topc ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_tops_3) ).
thf(1732,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( D @ ( B @ k6_pre_topc ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(191,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_struct_0 ) ) )
=> ( A @ ( B @ ( A @ k1_tex_2 ) @ v4_tex_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_tex_4) ).
thf(2121,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_struct_0 ) ) )
=> ( A @ ( B @ ( A @ k1_tex_2 ) @ v4_tex_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ( ( C
= ( B @ ( A @ k6_tex_4 ) ) )
<=> ( ( C @ u1_struct_0 )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_tex_4) ).
thf(2729,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ( ( ( ( C @ u1_struct_0 )
= B )
=> ( C
= ( B @ ( A @ k6_tex_4 ) ) ) )
& ( ( C
= ( B @ ( A @ k6_tex_4 ) ) )
=> ( ( C @ u1_struct_0 )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(1727,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(200,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_tex_4) ).
thf(2176,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(225,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tsp_1 ) )
| ( A @ ( B @ v1_tsp_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tsp_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tsp_1) ).
thf(2292,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tsp_1 ) )
| ( A @ ( B @ v1_tsp_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tsp_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(5762,plain,
sk327 @ v2_pcomps_1,
inference(cnfConj,[status(thm)],[5758]) ).
thf(414,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tex_2 ) )
<=> ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_tex_2) ).
thf(3257,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ( A @ ( B @ v4_tex_2 ) ) )
& ( ( A @ ( B @ v4_tex_2 ) )
=> ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(4872,plain,
( ( k22_borsuk_1 @ v2_pre_topc )
& ( k22_borsuk_1 @ v1_pre_topc )
& ~ ( k22_borsuk_1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[4871]) ).
thf(4874,plain,
k22_borsuk_1 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[4872]) ).
thf(7891,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,959]) ).
thf(7892,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[7891]) ).
thf(7893,plain,
! [A: $i] :
( ( A @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( A @ sk5 ) @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(pattern_uni,[status(thm)],[7892:[bind(A,$thf( sk1 ))]]) ).
thf(8040,plain,
! [A: $i] :
( ( A @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( A @ sk5 ) @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[7893]) ).
thf(898,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( A @ ( C @ v2_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_tex_3) ).
thf(5979,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( A @ ( C @ v2_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(637,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_tdlat_3 )
<=> ( ( A @ u1_pre_topc )
= ( A @ u1_struct_0 @ k1_pcomps_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tdlat_3) ).
thf(4489,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( ( A @ u1_pre_topc )
= ( A @ u1_struct_0 @ k1_pcomps_1 ) )
=> ( A @ v1_tdlat_3 ) )
& ( ( A @ v1_tdlat_3 )
=> ( ( A @ u1_pre_topc )
= ( A @ u1_struct_0 @ k1_pcomps_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(2894,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(434,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) )
= ( B @ ( A @ u1_struct_0 @ k2_borsuk_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_borsuk_1) ).
thf(3343,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) )
= ( B @ ( A @ u1_struct_0 @ k2_borsuk_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(9652,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk174 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2888,3668]) ).
thf(9653,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk174 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9652]) ).
thf(9660,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk174 )
!= B )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9653]) ).
thf(9677,plain,
! [A: $i] :
( ( ( A @ sk174 @ k1_zfmisc_1 )
!= A )
| ~ ( A @ sk174 @ k1_zfmisc_1 @ ( A @ sk174 @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9660]) ).
thf(585,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tex_4) ).
thf(4116,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ~ ( B @ ( D @ r2_hidden ) ) )
& ( ~ ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(614,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tdlat_3) ).
thf(4340,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(549,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( D @ ( A @ k1_tsep_1 ) ) )
= ( C @ ( D @ ( A @ k1_tsep_1 ) ) @ ( B @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( D @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_tsep_1) ).
thf(3888,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( D @ ( A @ k1_tsep_1 ) ) )
= ( C @ ( D @ ( A @ k1_tsep_1 ) ) @ ( B @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) )
= ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( D @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ k2_tsep_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(2997,plain,
! [A: $i] : ( A @ sk179 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2995]) ).
thf(7161,plain,
! [B: $i,A: $i] :
( ( ( A @ sk179 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2997,3046]) ).
thf(7162,plain,
! [B: $i,A: $i] :
( ( A @ sk179 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7161]) ).
thf(7165,plain,
! [B: $i,A: $i] :
( ( A @ sk179 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[7162]) ).
thf(266,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( ( B @ ( E @ v3_pre_topc ) )
<=> ( A @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tsep_1) ).
thf(2524,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( ( ( A @ ( D @ v3_pre_topc ) )
=> ( B @ ( E @ v3_pre_topc ) ) )
& ( ( B @ ( E @ v3_pre_topc ) )
=> ( A @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(241,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v1_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tdlat_3) ).
thf(2376,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ v1_tdlat_3 ) )
& ( ( A @ v1_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(5239,plain,
( ( sk289 @ v1_pre_topc )
& ( sk289 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5238]) ).
thf(5241,plain,
sk289 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5239]) ).
thf(158,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(1916,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(2788,plain,
~ ? [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[2787]) ).
thf(2789,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2788]) ).
thf(855,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v1_tex_3 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ~ ( C @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_tex_3) ).
thf(5844,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v1_tex_3 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ~ ( C @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(134,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B
= ( A @ u1_struct_0 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_3) ).
thf(1752,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B
= ( A @ u1_struct_0 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(681,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_tsep_1) ).
thf(4801,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(5831,plain,
sk330 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5828]) ).
thf(810,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v2_t_0topsp )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_tsp_1) ).
thf(5612,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v2_t_0topsp )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(463,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ k1_pre_topc @ v6_compts_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_compts_1) ).
thf(3458,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ k1_pre_topc @ v6_compts_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(911,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tsp_2) ).
thf(6019,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(705,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_tsep_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_tsep_1) ).
thf(4946,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v1_tsep_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(719,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( A @ ( C @ v5_tex_2 ) )
& ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_tex_2) ).
thf(5022,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( A @ ( C @ v5_tex_2 ) )
& ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(406,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( ( A @ ( B @ v2_tsp_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tsp_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_tsp_2) ).
thf(3213,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tsp_2 ) ) ) )
=> ( A @ ( B @ v2_tsp_2 ) ) )
& ( ( A @ ( B @ v2_tsp_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v1_tsp_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(825,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_tsp_1) ).
thf(5720,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(440,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k5_tex_4 ) @ v4_tex_4 ) )
& ( B @ ( A @ k5_tex_4 ) @ v3_tdlat_3 )
& ( B @ ( A @ k5_tex_4 ) @ v2_tdlat_3 )
& ( B @ ( A @ k5_tex_4 ) @ v2_pre_topc )
& ( B @ ( A @ k5_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k5_tex_4 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_tex_4) ).
thf(3372,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k5_tex_4 ) @ v4_tex_4 ) )
& ( B @ ( A @ k5_tex_4 ) @ v3_tdlat_3 )
& ( B @ ( A @ k5_tex_4 ) @ v2_tdlat_3 )
& ( B @ ( A @ k5_tex_4 ) @ v2_pre_topc )
& ( B @ ( A @ k5_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k5_tex_4 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(660,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
<=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_tsep_1) ).
thf(4662,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(790,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_4 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_4) ).
thf(5456,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_4 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(883,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( B @ m1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_tsep_1) ).
thf(5933,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( B @ m1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(347,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tex_3) ).
thf(2970,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(428,axiom,
! [A: $i] :
( ( A @ k2_pcomps_1 )
= ( A @ k1_pcomps_1 @ ( A @ g1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_pcomps_1) ).
thf(3319,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 )
= ( A @ k1_pcomps_1 @ ( A @ g1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(500,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(3636,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(409,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_tsep_1) ).
thf(3234,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(341,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( B @ ( D @ v1_tops_1 ) )
<=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tex_3) ).
thf(2938,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
=> ( B @ ( D @ v1_tops_1 ) ) )
& ( ( B @ ( D @ v1_tops_1 ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(606,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v5_tex_2 ) )
& ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc24_tex_3) ).
thf(4283,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v5_tex_2 ) )
& ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ v3_pre_topc ) )
<=> ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_tops_2) ).
thf(1784,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( C @ v3_pre_topc ) )
=> ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(796,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ ( A @ r1_tsep_1 ) ) )
& ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_tsep_1) ).
thf(5488,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ ( A @ r1_tsep_1 ) ) )
& ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ ( A @ r1_tsep_1 ) ) )
& ( C @ ( D @ ( A @ r1_tsep_1 ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(204,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ( A @ v2_t_0topsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tsp_1) ).
thf(2188,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
=> ( ( ( A @ v2_t_0topsp )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ( A @ v2_t_0topsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(886,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tsp_2 ) )
<=> ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m2_tsp_1 ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) )
& ( B @ v2_t_0topsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_tsp_2) ).
thf(5940,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m2_tsp_1 ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) )
& ( B @ v2_t_0topsp ) )
=> ( A @ ( B @ v2_tsp_2 ) ) )
& ( ( A @ ( B @ v2_tsp_2 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m2_tsp_1 ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) ) )
& ( B @ v2_t_0topsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(557,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( A @ ( C @ v2_tex_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_tex_2) ).
thf(3945,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
& ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( A @ ( C @ v2_tex_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(724,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_tex_3) ).
thf(5050,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(97,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_4) ).
thf(1535,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(866,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v2_pre_topc )
=> ~ ( B @ v2_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_tex_2) ).
thf(5876,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v2_pre_topc )
=> ~ ( B @ v2_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(622,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v3_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_tex_3) ).
thf(4381,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v3_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(759,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc17_tex_2) ).
thf(5271,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(650,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc27_tex_2) ).
thf(4590,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v3_realset2 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(94,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) )
=> ( A @ ( B @ v3_tex_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_tex_4) ).
thf(1520,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) )
=> ( A @ ( B @ v3_tex_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(5752,plain,
sk326 @ v3_pcomps_1,
inference(cnfConj,[status(thm)],[5749]) ).
thf(722,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tsep_1) ).
thf(5039,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(877,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ v2_pre_topc )
& ~ ( A @ k3_t_0topsp @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_t_0topsp) ).
thf(5908,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k3_t_0topsp @ v2_pre_topc )
& ~ ( A @ k3_t_0topsp @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(859,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_tdlat_3) ).
thf(5859,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(687,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ~ ( A @ ( B @ v2_tex_3 ) ) )
=> ( A @ v3_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_tex_3) ).
thf(4822,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ~ ( A @ ( B @ v2_tex_3 ) ) )
=> ( A @ v3_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(575,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tdlat_3) ).
thf(4060,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_pre_topc) ).
thf(1765,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_pre_topc @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(604,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_tdlat_3 )
=> ~ ( B @ v1_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc21_tex_2) ).
thf(4273,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_tdlat_3 )
=> ~ ( B @ v1_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(747,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_tsep_1) ).
thf(5185,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_borsuk_1) ).
thf(3773,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(6,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_tops_1) ).
thf(935,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc ) ),
inference(cnf,[status(esa)],[935]) ).
thf(721,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k3_t_0topsp @ u1_pre_topc )
= ( A @ a_1_0_t_0topsp ) )
& ( ( A @ k3_t_0topsp @ u1_struct_0 )
= ( A @ k2_t_0topsp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_t_0topsp) ).
thf(5033,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k3_t_0topsp @ u1_pre_topc )
= ( A @ a_1_0_t_0topsp ) )
& ( ( A @ k3_t_0topsp @ u1_struct_0 )
= ( A @ k2_t_0topsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(527,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tex_3) ).
thf(3751,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(211,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ ( A @ k1_struct_0 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_borsuk_1) ).
thf(2220,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ ( A @ k1_struct_0 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(124,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v1_tops_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_tops_3) ).
thf(1707,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v1_tops_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(735,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_topmetr) ).
thf(5118,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(774,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ v4_tdlat_3 ) )
=> ( A @ v5_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_tdlat_3) ).
thf(5363,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ v4_tdlat_3 ) )
=> ( A @ v5_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(3051,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(793,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc44_tex_2) ).
thf(5471,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(228,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ ( A @ k1_tex_2 ) ) )
<=> ( ( C @ u1_struct_0 )
= ( B @ ( A @ k1_struct_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tex_2) ).
thf(2308,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( ( C @ u1_struct_0 )
= ( B @ ( A @ k1_struct_0 ) ) )
=> ( C
= ( B @ ( A @ k1_tex_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_tex_2 ) ) )
=> ( ( C @ u1_struct_0 )
= ( B @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(588,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) )
=> ( ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
<=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_tsep_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( F @ m1_pre_topc ) )
& ( A
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ( A
!= ( E @ ( D @ ( A @ k1_tsep_1 ) ) ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_tsep_1) ).
thf(4149,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) )
=> ( ( ( ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_tsep_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( F @ m1_pre_topc ) )
& ( A
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ( A
!= ( E @ ( D @ ( A @ k1_tsep_1 ) ) ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_borsuk_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_tsep_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( F @ m1_pre_topc ) )
& ( A
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ( A
!= ( E @ ( D @ ( A @ k1_tsep_1 ) ) ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(4218,plain,
sk238 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[4215]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k19_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k19_borsuk_1) ).
thf(5086,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k19_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(2920,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) ),
inference(cnfConj,[status(thm)],[2919]) ).
thf(8490,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2920,6688]) ).
thf(8491,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) ) ),
inference(simp,[status(thm)],[8490]) ).
thf(8492,plain,
( ( sk1 @ ( sk1 @ u1_struct_0 @ sk175 @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( sk1 @ u1_struct_0 @ sk175 @ v3_pre_topc ) ) ),
inference(pattern_uni,[status(thm)],[8491:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( sk1 @ u1_struct_0 @ sk175 ))]]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(3487,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(175,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_tops_3) ).
thf(2055,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(657,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
<=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tex_3) ).
thf(4640,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
=> ( A @ ( B @ v2_tex_3 ) ) )
& ( ( A @ ( B @ v2_tex_3 ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[962]) ).
thf(668,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_tex_3) ).
thf(4704,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(750,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_3) ).
thf(5212,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(2642,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(358,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_tex_3) ).
thf(3038,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
<=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tops_1) ).
thf(1574,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ k6_pre_topc ) @ v2_tops_1 ) )
=> ( A @ ( B @ v3_tops_1 ) ) )
& ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(3515,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(868,axiom,
k22_borsuk_1 @ l1_pre_topc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_borsuk_1) ).
thf(5880,plain,
k22_borsuk_1 @ l1_pre_topc,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(608,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc20_tex_2) ).
thf(4300,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v5_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(3586,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tops_3) ).
thf(1376,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ u1_struct_0 ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(863,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( A @ ( C @ v1_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tex_3) ).
thf(5870,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( A @ ( C @ v1_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(679,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( C @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tsep_1) ).
thf(4790,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( C @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(250,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v6_compts_1 ) ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_compts_1) ).
thf(2415,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v6_compts_1 ) ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(733,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc26_tex_2) ).
thf(5103,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(417,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v2_tsp_2 ) ) ) )
& ( A @ ( B @ v1_tsp_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tsp_2) ).
thf(3270,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v2_tsp_2 ) ) ) )
& ( A @ ( B @ v1_tsp_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(217,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_tops_1) ).
thf(2257,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[978]) ).
thf(161,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ ( A @ k1_struct_0 ) @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k1_struct_0 ) @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_tex_4) ).
thf(1933,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k5_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ ( A @ k1_struct_0 ) @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k1_struct_0 ) @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(654,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc16_tex_2) ).
thf(4616,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
thf(1801,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ ( B @ v1_tops_1 ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_tops_3) ).
thf(1307,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ ( B @ v1_tops_1 ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(749,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc43_tex_2) ).
thf(5202,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(729,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_tex_3) ).
thf(5082,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(602,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_tex_3) ).
thf(4264,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(301,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( B @ ( D @ v3_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_tops_3) ).
thf(2757,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( C = D ) )
=> ( B @ ( D @ v3_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(613,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
<=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_tex_3) ).
thf(4332,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
=> ( A @ ( B @ v4_tex_3 ) ) )
& ( ( A @ ( B @ v4_tex_3 ) )
=> ( A @ ( C @ v3_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(52432,plain,
( ( ( sk329 @ v3_compts_1 )
!= ( sk1 @ v3_compts_1 ) )
| ( sk2 != sk1 )
| ~ $true
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk1 @ v2_t_0topsp ) ),
inference(paramod_ordered,[status(thm)],[5788,47442]) ).
thf(52433,plain,
( ( ( sk329 @ v3_compts_1 )
!= ( sk1 @ v3_compts_1 ) )
| ( sk2 != sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk1 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[52432]) ).
thf(52436,plain,
( ( sk329 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk1 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[52433]) ).
thf(607,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_2 ) ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
<=> ( A @ ( C @ v3_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_tex_3) ).
thf(4296,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v3_tex_3 ) )
=> ( A @ ( B @ v1_tex_3 ) ) )
& ( ( A @ ( B @ v1_tex_3 ) )
=> ( A @ ( C @ v3_tex_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(3583,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(224,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k2_pre_topc @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_tops_1) ).
thf(2289,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k2_pre_topc @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(781,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_tex_2) ).
thf(5410,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_2 ) )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(26,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_tops_1) ).
thf(1061,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(462,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_tex_4) ).
thf(3456,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(9637,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2996,3668]) ).
thf(9638,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9637]) ).
thf(9668,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk179 )
!= B )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9638]) ).
thf(9674,plain,
! [A: $i] :
( ( ( A @ sk179 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ~ ( A @ sk179 @ k1_zfmisc_1 @ ( A @ sk179 @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9668]) ).
thf(18558,plain,
! [A: $i] :
( ( ( A @ sk179 )
!= A )
| ~ ( A @ sk179 @ k1_zfmisc_1 @ ( A @ sk179 @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9674]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).
thf(2824,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(665,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v2_tdlat_3 )
=> ~ ( A @ ( B @ v4_tex_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tex_4) ).
thf(4694,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v2_tdlat_3 )
=> ~ ( A @ ( B @ v4_tex_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(4635,plain,
sk264 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[4632]) ).
thf(201,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v3_tex_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_tex_2) ).
thf(2182,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v3_tex_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(6004,plain,
sk338 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[6001]) ).
thf(314,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_tdlat_3) ).
thf(2812,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) )
=> ( A @ v3_tdlat_3 ) )
& ( ( A @ v3_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_t_0topsp )
<=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( ~ ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_t_0topsp) ).
thf(1080,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( ~ ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) )
=> ( A @ v2_t_0topsp ) )
& ( ( A @ v2_t_0topsp )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( ~ ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(695,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tdlat_3) ).
thf(4882,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(2343,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ m1_borsuk_1 ) )
& ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ v2_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k20_borsuk_1) ).
thf(4462,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ m1_borsuk_1 ) )
& ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ v2_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(700,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tex_3) ).
thf(4911,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(903,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v2_tex_3 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_tex_3) ).
thf(5994,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v2_tex_3 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(368,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k7_tex_4 ) @ ( B @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_tex_4) ).
thf(3073,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k7_tex_4 ) @ ( B @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(576,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v4_tex_3 ) )
& ( A @ ( B @ v4_tex_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v4_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tex_3) ).
thf(4064,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v4_tex_3 ) )
& ( A @ ( B @ v4_tex_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v4_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(686,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v2_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_tex_3) ).
thf(4818,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v2_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(3570,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk204 @ v1_tex_2 ) )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk204 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3569]) ).
thf(3572,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ sk204 @ v1_tex_2 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3570]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(1909,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(630,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tex_3) ).
thf(4452,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(4993,plain,
sk281 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[4991]) ).
thf(5987,plain,
sk337 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5984]) ).
thf(274,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( A @ ( B @ v3_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) )
=> ( A @ ( B @ v3_tex_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tex_4) ).
thf(2578,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( A @ ( B @ v3_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) )
=> ( A @ ( B @ v3_tex_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[966]) ).
thf(670,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_borsuk_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_tsep_1) ).
thf(4720,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_borsuk_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(4232,plain,
sk239 @ v3_tdlat_3,
inference(cnfConj,[status(thm)],[4228]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_tex_4) ).
thf(1213,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) ) )
& ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v1_tex_4 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B
= ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9256,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[4488,9190]) ).
thf(9294,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 )
!= sk1 )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[9256]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) )
& ~ ( B @ ( A @ k6_pre_topc ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_tex_4) ).
thf(2086,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) )
& ~ ( B @ ( A @ k6_pre_topc ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(555,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_tex_3) ).
thf(3917,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v4_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tsp_2 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v1_tsp_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tsp_2) ).
thf(1000,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tsp_2 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v1_tsp_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(592,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc37_tex_2) ).
thf(4196,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(913,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_compts_1 )
=> ( A @ v2_pcomps_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_pcomps_1) ).
thf(6029,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_compts_1 )
=> ( A @ v2_pcomps_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(8455,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2920,6905]) ).
thf(8456,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8455]) ).
thf(8457,plain,
( ( sk1 @ ( sk1 @ u1_struct_0 @ sk175 @ v3_pre_topc ) )
| ~ ( sk1 @ ( sk1 @ u1_struct_0 @ sk175 @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
inference(pattern_uni,[status(thm)],[8456:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( sk1 @ u1_struct_0 @ sk175 ))]]) ).
thf(5742,plain,
sk324 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5738]) ).
thf(344,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_tops_3) ).
thf(2962,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(5254,plain,
sk290 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5248]) ).
thf(838,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v2_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_tex_3) ).
thf(5775,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
& ( C @ ( B @ v2_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(5931,plain,
sk334 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5928]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_tex_2 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v4_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_tex_2) ).
thf(2725,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_tex_2 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v4_tex_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(108,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) )
| ( C = D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_tex_2) ).
thf(1594,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) )
| ( C = D ) ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) )
& ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_xboole_0 ) )
| ( C = D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(174,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(2051,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(3423,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(9480,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ $true
| ~ ( A @ l1_pre_topc ) ),
inference(paramod_ordered,[status(thm)],[918,971]) ).
thf(9481,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk6 ) @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[9480]) ).
thf(9482,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[9481:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(12515,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[9482,922]) ).
thf(12516,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[12515]) ).
thf(12554,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ~ $true
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk2 @ v2_t_0topsp ) ),
inference(paramod_ordered,[status(thm)],[12516,6486]) ).
thf(12555,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk2 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[12554]) ).
thf(12556,plain,
( ( sk329 != sk1 )
| ( sk1 @ ( sk1 @ ( sk2 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ( sk2 @ v2_t_0topsp ) ),
inference(pattern_uni,[status(thm)],[12555:[bind(A,$thf( sk1 @ ( sk2 @ sk6 ) ))]]) ).
thf(536,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_tex_3) ).
thf(3806,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(240,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
<=> ? [C: $i] :
( ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ r1_tarski ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_tops_3) ).
thf(2369,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ r1_tarski ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ v3_tops_1 ) ) )
& ( ( A @ ( B @ v3_tops_1 ) )
=> ? [C: $i] :
( ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( C @ v4_pre_topc ) )
& ( C @ ( B @ r1_tarski ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_subset_1) ).
thf(1015,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(688,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_2 ) ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
<=> ( A @ ( C @ v4_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_tex_3) ).
thf(4827,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v4_tex_3 ) )
=> ( A @ ( B @ v2_tex_3 ) ) )
& ( ( A @ ( B @ v2_tex_3 ) )
=> ( A @ ( C @ v4_tex_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[970]) ).
thf(287,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v3_tex_3 ) ) ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_tex_3) ).
thf(2633,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v3_tex_3 ) ) ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(856,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tsp_1) ).
thf(5849,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_t_0topsp )
<=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tsp_1) ).
thf(1477,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) )
=> ( A @ v2_t_0topsp ) )
& ( ( A @ v2_t_0topsp )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B != C ) ) ) )
| ( A @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(3706,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(707,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ m1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tsep_1) ).
thf(4954,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ m1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(2967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(244,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v2_tops_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tops_3) ).
thf(2390,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v2_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(3512,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(395,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(3178,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(822,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v5_tex_2 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc23_tex_3) ).
thf(5693,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v5_tex_2 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(3348,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(731,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc31_tex_2) ).
thf(5089,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(547,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k2_tsep_1 ) ) ) )
<=> ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tsep_1) ).
thf(3876,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) )
=> ( D
= ( C @ ( B @ ( A @ k2_tsep_1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k2_tsep_1 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(710,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
<=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_tsep_1) ).
thf(4965,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(326,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_tops_3) ).
thf(2867,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(472,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(3490,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(3380,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
<=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ~ ( A @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_pre_topc) ).
thf(1562,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ~ ( A @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(783,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_tsep_1) ).
thf(5424,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(400,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ v3_realset2 )
& ( A @ ( B @ ( A @ k1_tex_2 ) @ v2_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_tex_2) ).
thf(3193,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ v3_realset2 )
& ( A @ ( B @ ( A @ k1_tex_2 ) @ v2_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(870,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_tsep_1) ).
thf(5886,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(5785,plain,
sk329 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[5784]) ).
thf(328,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B
!= ( C @ ( A @ k1_struct_0 ) ) ) )
& ( A @ k15_borsuk_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_borsuk_1) ).
thf(2878,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B
!= ( C @ ( A @ k1_struct_0 ) ) ) )
& ( A @ k15_borsuk_1 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(420,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_pre_topc) ).
thf(3292,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(673,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ u1_struct_0 )
= ( A @ k1_lopclset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_lopclset) ).
thf(4741,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ u1_struct_0 )
= ( A @ k1_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(821,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_tex_3) ).
thf(5688,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(890,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_lopclset @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lopclset) ).
thf(5959,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_lopclset @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(869,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_tdlat_3) ).
thf(5881,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(685,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ~ ( A @ ( B @ v1_tex_3 ) ) )
=> ( A @ v1_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_tex_3) ).
thf(4813,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ~ ( A @ ( B @ v1_tex_3 ) ) )
=> ( A @ v1_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k5_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k5_tex_4 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_tex_4) ).
thf(2124,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k5_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k5_tex_4 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(6130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[919,936]) ).
thf(6131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[6130]) ).
thf(6132,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ ( A @ ( sk1 @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[6131:[bind(A,$thf( sk1 ))]]) ).
thf(6170,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ ( A @ ( sk1 @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(simp,[status(thm)],[6132]) ).
thf(6190,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ ( A @ ( sk1 @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6170,922]) ).
thf(6191,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ ( A @ ( sk1 @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ ( A @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6190]) ).
thf(5952,plain,
sk336 @ l1_pre_topc,
inference(cnf,[status(esa)],[5951]) ).
thf(6941,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
!= ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ $true
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[6483,6905]) ).
thf(6942,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
!= ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6941]) ).
thf(6960,plain,
! [B: $i,A: $i] :
( ( sk1 != sk1 )
| ( ( A @ ( sk1 @ k1_struct_0 ) )
!= ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ ( B @ v3_pre_topc ) ) ),
inference(simp,[status(thm)],[6942]) ).
thf(6962,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ k1_struct_0 ) )
!= ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ ( B @ v3_pre_topc ) ) ),
inference(simp,[status(thm)],[6960]) ).
thf(819,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_tex_4) ).
thf(5678,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
=> ( B @ v2_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(645,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ~ ( A @ ( B @ v4_tex_3 ) ) )
=> ( A @ v3_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_tex_3) ).
thf(4566,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ~ ( A @ ( B @ v4_tex_3 ) ) )
=> ( A @ v3_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(692,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_tex_3) ).
thf(4859,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(207,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_pre_topc) ).
thf(2202,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(6074,plain,
( ( ( sk320 @ v2_tdlat_3 )
!= ( sk264 @ v2_tdlat_3 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5674,4633]) ).
thf(6075,plain,
( ( sk320 @ v2_tdlat_3 )
!= ( sk264 @ v2_tdlat_3 ) ),
inference(simp,[status(thm)],[6074]) ).
thf(6076,plain,
sk320 != sk264,
inference(simp,[status(thm)],[6075]) ).
thf(879,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k15_borsuk_1 @ m1_borsuk_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_borsuk_1) ).
thf(5916,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k15_borsuk_1 @ m1_borsuk_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k6_pre_topc ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(1018,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k6_pre_topc ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(271,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_tops_1) ).
thf(2564,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(3278,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(648,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v2_tdlat_3 )
=> ( B @ v3_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc22_tex_2) ).
thf(4581,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v2_tdlat_3 )
=> ( B @ v3_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(15251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ~ ( C @ ( A @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3473,9613]) ).
thf(15252,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[15251:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(835,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_tdlat_3) ).
thf(5763,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(772,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pre_topc) ).
thf(5358,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(739,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) ) )
<=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tex_3) ).
thf(5133,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) ) ) )
& ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(902,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k4_tdlat_1 )
= ( A @ k8_tdlat_1 ) )
=> ( A @ v4_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_tdlat_3) ).
thf(5991,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k4_tdlat_1 )
= ( A @ k8_tdlat_1 ) )
=> ( A @ v4_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(3571,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ sk204 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3570]) ).
thf(143,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tdlat_3) ).
thf(1798,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(824,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_tsp_2) ).
thf(5716,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ~ ( A @ ( B @ v2_tsp_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(570,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v2_t_0topsp )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_tsp_1) ).
thf(4035,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v2_t_0topsp )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(195,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_tops_3) ).
thf(2143,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(541,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ( A @ v2_compts_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v5_compts_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_compts_1) ).
thf(3833,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ( A @ v2_compts_1 )
& ( A @ v3_compts_1 ) )
=> ( A @ v5_compts_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(382,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v4_tex_4 ) )
& ~ ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tex_4) ).
thf(3129,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_4 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v4_tex_4 ) )
& ~ ( B @ v2_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(73,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_tdlat_3) ).
thf(1368,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) )
=> ( A @ v4_tdlat_3 ) )
& ( ( A @ v4_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(697,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_tsep_1 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc29_tex_2) ).
thf(4894,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v1_tsep_1 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(621,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ~ ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v3_tex_3 ) )
& ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( ( A @ ( C @ v3_tex_3 ) )
| ( A @ ( B @ v3_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_tex_3) ).
thf(4377,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ~ ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v3_tex_3 ) )
& ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
& ( ( A @ ( C @ v3_tex_3 ) )
| ( A @ ( B @ v3_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(611,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ l1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pre_topc) ).
thf(4324,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ l1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(841,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k4_tdlat_1 )
= ( A @ k12_tdlat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_tdlat_3) ).
thf(5790,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k4_tdlat_1 )
= ( A @ k12_tdlat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[972]) ).
thf(58119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( E @ ( D @ k2_xboole_0 ) ) )
| ~ ( C @ ( D @ k3_xboole_0 ) @ ( A @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3473,58083]) ).
thf(58120,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( A @ k3_xboole_0 ) @ ( A @ ( B @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[58119:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(789,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_compts_1 )
<=> ( A @ ( A @ k2_pre_topc @ v6_compts_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_compts_1) ).
thf(5452,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ ( A @ k2_pre_topc @ v6_compts_1 ) )
=> ( A @ v2_compts_1 ) )
& ( ( A @ v2_compts_1 )
=> ( A @ ( A @ k2_pre_topc @ v6_compts_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
<=> ( A @ ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(1748,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(624,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4398,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(4399,plain,
sk249 @ v1_xboole_0,
inference(cnf,[status(esa)],[4398]) ).
thf(7163,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk249 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4399,3046]) ).
thf(7164,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk249 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7163]) ).
thf(7166,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk249 ),
inference(simp,[status(thm)],[7164]) ).
thf(324,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ k16_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_borsuk_1) ).
thf(2863,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ k16_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(809,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc34_tex_2) ).
thf(5602,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(5514,plain,
sk308 @ l2_quantal1,
inference(cnf,[status(esa)],[5513]) ).
thf(2958,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[2957]) ).
thf(2959,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[2958]) ).
thf(2960,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[2959]) ).
thf(2961,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk177 ) )
= A ),
inference(cnf,[status(esa)],[2960]) ).
thf(57758,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk177 ) )
= A ),
inference(lifteq,[status(thm)],[2961]) ).
thf(5250,plain,
~ ( sk290 @ v3_realset2 ),
inference(cnfConj,[status(thm)],[5248]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(3112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(703,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ~ ( ( A @ ( B @ v2_tex_2 ) )
& ( ( B @ u1_struct_0 )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_tex_2) ).
thf(4937,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ~ ( ( A @ ( B @ v2_tex_2 ) )
& ( ( B @ u1_struct_0 )
= ( A @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(778,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) ) )
=> ( ( B @ ( A @ r1_borsuk_1 ) )
=> ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ r1_borsuk_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_borsuk_1) ).
thf(5388,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) ) )
=> ( ( B @ ( A @ r1_borsuk_1 ) )
=> ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ r1_borsuk_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(619,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_tsep_1) ).
thf(4366,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
& ( A
= ( C @ ( B @ ( A @ k1_tsep_1 ) ) ) ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_pre_topc) ).
thf(1605,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(276,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_tex_2) ).
thf(2588,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(706,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc24_tex_2) ).
thf(4950,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(138,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_tops_3) ).
thf(1780,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(405,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tsp_1) ).
thf(3209,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_t_0topsp )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(3246,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(615,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_tdlat_3) ).
thf(4346,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(128,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_tex_2) ).
thf(1716,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_tex_2 ) ) ) )
=> ( A @ ( B @ v5_tex_2 ) ) )
& ( ( A @ ( B @ v5_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_tex_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tex_4) ).
thf(1186,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(717,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_tsep_1) ).
thf(5015,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_tops_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_tops_1) ).
thf(1038,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_tops_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5753,plain,
sk326 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5749]) ).
thf(595,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc28_tex_2) ).
thf(4222,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(381,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(3127,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_tex_2 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_tex_2) ).
thf(1658,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_tex_2 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(279,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lopclset) ).
thf(2599,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(672,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ~ ( A @ ( B @ v3_tex_3 ) ) )
=> ( A @ v1_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_tex_3) ).
thf(4737,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ~ ( A @ ( B @ v3_tex_3 ) ) )
=> ( A @ v1_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(813,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v2_t_0topsp )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tsp_1) ).
thf(5638,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v2_t_0topsp )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(788,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_tdlat_3 )
=> ( A @ v3_tdlat_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tdlat_3) ).
thf(5450,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_tdlat_3 )
=> ( A @ v3_tdlat_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(4875,plain,
k22_borsuk_1 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[4872]) ).
thf(290,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
=> ( ( D = E )
| ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_borsuk_1) ).
thf(2656,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
=> ( ( D = E )
| ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(356,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) ) )
=> ( ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( C @ v1_tops_3 ) ) )
<=> ( A @ ( D @ v1_tops_3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_tops_3) ).
thf(3019,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) ) )
=> ( ( ( A @ ( D @ v1_tops_3 ) )
=> ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( C @ v1_tops_3 ) ) ) )
& ( ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( C @ v1_tops_3 ) ) )
=> ( A @ ( D @ v1_tops_3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(820,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v1_borsuk_1 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tsep_1) ).
thf(5684,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v1_borsuk_1 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(459,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) ) )
=> ( ( B @ ( A @ r2_borsuk_1 ) )
=> ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ r2_borsuk_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_borsuk_1) ).
thf(3448,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) ) )
=> ( ( B @ ( A @ r2_borsuk_1 ) )
=> ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ r2_borsuk_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(4522,plain,
~ ( sk255 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4520]) ).
thf(828,axiom,
! [A: $i] : ( A @ k2_pcomps_1 @ l1_pre_topc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pcomps_1) ).
thf(5731,plain,
! [A: $i] : ( A @ k2_pcomps_1 @ l1_pre_topc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) )
= ( B @ ( C @ ( A @ k1_tsep_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_tsep_1) ).
thf(4190,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) )
= ( B @ ( C @ ( A @ k1_tsep_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(539,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_tex_3) ).
thf(3818,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(85,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
| ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_tex_4) ).
thf(1452,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
| ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(378,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( A @ ( C @ v2_tops_1 ) )
<=> ( B @ ( D @ v2_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_tops_3) ).
thf(3114,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( B @ ( D @ v2_tops_1 ) )
=> ( A @ ( C @ v2_tops_1 ) ) )
& ( ( A @ ( C @ v2_tops_1 ) )
=> ( B @ ( D @ v2_tops_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(878,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v1_borsuk_1 ) )
| ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v2_t_0topsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_tsp_1) ).
thf(5912,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ( B @ v2_t_0topsp )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A @ ( C @ v1_borsuk_1 ) )
| ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ v2_t_0topsp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(5677,plain,
sk320 @ v1_tdlat_3,
inference(cnfConj,[status(thm)],[5672]) ).
thf(6091,plain,
( ( ( sk320 @ v1_tdlat_3 )
!= ( sk290 @ v1_tdlat_3 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5677,5253]) ).
thf(6092,plain,
( ( sk320 @ v1_tdlat_3 )
!= ( sk290 @ v1_tdlat_3 ) ),
inference(simp,[status(thm)],[6091]) ).
thf(6093,plain,
sk320 != sk290,
inference(simp,[status(thm)],[6092]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_tops_1) ).
thf(1262,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_tops_1) ).
thf(1235,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(221,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( C @ ( B @ r1_tarski ) )
& ~ ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tex_4) ).
thf(2276,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( C @ ( B @ r1_tarski ) )
& ~ ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v4_pre_topc ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( C @ ( B @ r1_tarski ) )
& ~ ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ~ ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(2128,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ~ ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(8204,plain,
! [B: $i,A: $i] :
( ( ( sk249 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ $true
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[4399,2789]) ).
thf(8205,plain,
! [B: $i,A: $i] :
( ( ( sk249 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[8204]) ).
thf(8206,plain,
! [A: $i] :
~ ( sk249 @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[8205:[bind(A,$thf( A )),bind(B,$thf( sk249 ))]]) ).
thf(8642,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2996,6688]) ).
thf(8643,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( B @ v3_pre_topc ) ) ),
inference(simp,[status(thm)],[8642]) ).
thf(8644,plain,
( ( sk1 @ ( sk1 @ u1_struct_0 @ sk179 @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( sk1 @ ( sk1 @ u1_struct_0 @ sk179 @ v3_pre_topc ) ) ),
inference(pattern_uni,[status(thm)],[8643:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( sk1 @ u1_struct_0 @ sk179 ))]]) ).
thf(498,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tex_2) ).
thf(3623,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(515,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_tops_3) ).
thf(3697,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(5675,plain,
sk320 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5672]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(3124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k16_borsuk_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_borsuk_1) ).
thf(4611,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k16_borsuk_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(3320,plain,
! [A: $i] :
( ( A @ k2_pcomps_1 )
= ( A @ k1_pcomps_1 @ ( A @ g1_pre_topc ) ) ),
inference(cnf,[status(esa)],[3319]) ).
thf(3321,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 @ ( A @ g1_pre_topc ) )
= ( A @ k2_pcomps_1 ) ),
inference(lifteq,[status(thm)],[3320]) ).
thf(9622,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ g1_pre_topc ) )
= ( A @ k2_pcomps_1 ) ),
inference(rewrite,[status(thm)],[3321,3197]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(1008,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(8379,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( B @ v2_t_0topsp )
| ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,960]) ).
thf(8380,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ( B @ v2_t_0topsp )
| ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[8379]) ).
thf(8381,plain,
! [A: $i] :
( ( A @ v2_t_0topsp )
| ~ ( A @ v3_struct_0 )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(pattern_uni,[status(thm)],[8380:[bind(A,$thf( sk1 ))]]) ).
thf(8433,plain,
! [A: $i] :
( ( A @ v2_t_0topsp )
| ~ ( A @ v3_struct_0 )
| ~ ( sk1 @ ( A @ m2_tsp_1 ) ) ),
inference(simp,[status(thm)],[8381]) ).
thf(808,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_tdlat_3) ).
thf(5596,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v5_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(12616,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[4488,12516]) ).
thf(12665,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 )
!= sk1 )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[12616]) ).
thf(80,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(1404,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(216,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_tex_4) ).
thf(2247,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) )
=> ( A @ ( B @ v1_tex_4 ) ) )
& ( ( A @ ( B @ v1_tex_4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(740,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc29_tex_3) ).
thf(5147,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(269,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ~ ( A @ ( B @ v3_tex_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tex_4) ).
thf(2558,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ~ ( A @ ( B @ v3_tex_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(6071,plain,
( ( ( sk298 @ v1_xboole_0 )
!= ( sk249 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4399,5362]) ).
thf(6072,plain,
( ( sk298 @ v1_xboole_0 )
!= ( sk249 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6071]) ).
thf(6073,plain,
sk298 != sk249,
inference(simp,[status(thm)],[6072]) ).
thf(599,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v1_tsep_1 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tsep_1) ).
thf(4246,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ( B @ ( C @ v1_tsep_1 ) ) )
=> ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(904,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_tsp_1 ) )
=> ( B @ l1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_tsp_1) ).
thf(5998,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_tsp_1 ) )
=> ( B @ l1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(437,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) )
<=> ( A @ ( B @ v2_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tex_2) ).
thf(3356,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( B @ v2_tex_2 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) ) )
& ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ v1_tex_2 ) )
=> ( A @ ( B @ v2_tex_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(5240,plain,
sk289 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5239]) ).
thf(165,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(1955,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(321,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_tdlat_3) ).
thf(2843,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= B ) ) )
=> ( A @ v3_tdlat_3 ) )
& ( ( A @ v3_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(196,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
<=> ? [C: $i] :
( ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_tops_3) ).
thf(2145,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ v1_tops_3 ) ) )
& ( ( A @ ( B @ v1_tops_3 ) )
=> ? [C: $i] :
( ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(15239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( D @ ( C @ k2_xboole_0 ) ) )
| ( A @ ( B @ k2_xboole_0 ) @ ( C @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3473,3399]) ).
thf(15240,plain,
! [B: $i,A: $i] : ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[15239:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(583,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ~ ( E @ v3_struct_0 ) )
=> ( ( ( B @ ( C @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) )
=> ( ( B @ ( E @ ( A @ k1_tsep_1 ) ) @ ( C @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) )
& ( E @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_tsep_1) ).
thf(4106,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ~ ( E @ v3_struct_0 ) )
=> ( ( ( B @ ( C @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( E @ m1_pre_topc ) )
& ( B @ ( D @ m1_pre_topc ) ) )
=> ( ( B @ ( E @ ( A @ k1_tsep_1 ) ) @ ( C @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) )
& ( E @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( C @ ( A @ k1_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(847,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tsp_2) ).
thf(5809,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(572,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_tex_3) ).
thf(4046,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v3_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(58111,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
!= ( C @ ( D @ k3_xboole_0 ) ) )
| ~ ( A @ ( E @ ( D @ k2_xboole_0 ) @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[12351,58083]) ).
thf(58112,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[58111:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ k2_xboole_0 ) ))]]) ).
thf(58248,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ r2_hidden ) ),
inference(simp,[status(thm)],[58112]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(1140,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4634,plain,
sk264 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[4632]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_tops_1) ).
thf(2807,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(390,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B
= ( A @ u1_struct_0 ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_tops_3) ).
thf(3156,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B
= ( A @ u1_struct_0 ) )
& ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(554,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v2_pre_topc )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tex_2) ).
thf(3914,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v2_pre_topc )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(3684,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(6607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
!= ( sk1 @ ( B @ v4_pre_topc ) ) )
| ( C @ ( B @ v4_pre_topc ) )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ $true
| ~ ( sk1 @ ( C @ m1_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[6483,6551]) ).
thf(6608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
!= ( sk1 @ ( B @ v4_pre_topc ) ) )
| ( C @ ( B @ v4_pre_topc ) )
| ~ ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ ( C @ m1_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6607]) ).
thf(6609,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( sk1 @ k1_struct_0 ) @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ m1_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( sk1 @ k1_struct_0 ) @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ),
inference(pattern_uni,[status(thm)],[6608:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk1 @ k1_struct_0 ) )),bind(C,$thf( C ))]]) ).
thf(6622,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( sk1 @ k1_struct_0 ) @ m1_subset_1 ) )
| ~ ( sk1 @ ( A @ m1_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( sk1 @ k1_struct_0 ) @ m1_subset_1 ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6609]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(1240,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4217,plain,
~ ( sk238 @ v3_realset2 ),
inference(cnfConj,[status(thm)],[4215]) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ~ ( C @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ( C @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ~ ( C @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ( C @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ~ ( A @ ( C @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[976]) ).
thf(445,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_borsuk_1) ).
thf(3400,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(2458,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(159,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tex_4 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v3_tex_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tex_4) ).
thf(1918,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tex_4 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v3_tex_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(908,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ v17_lattices ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lopclset) ).
thf(6013,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ v17_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(715,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc41_tex_2) ).
thf(4997,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
=> ( ( A @ ( B @ v5_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(589,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_pre_topc) ).
thf(4185,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(6936,plain,
! [A: $i] :
( ( ( A @ sk179 @ v1_xboole_0 )
!= ( sk298 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2997,5362]) ).
thf(6937,plain,
! [A: $i] :
( ( A @ sk179 @ v1_xboole_0 )
!= ( sk298 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6936]) ).
thf(6938,plain,
! [A: $i] :
( ( A @ sk179 )
!= sk298 ),
inference(simp,[status(thm)],[6937]) ).
thf(499,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( D
= ( B @ u1_struct_0 ) ) )
=> ( ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( D @ v1_tops_1 ) ) )
<=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_tops_3) ).
thf(3625,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( D
= ( B @ u1_struct_0 ) ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
=> ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( D @ v1_tops_1 ) ) ) )
& ( ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( D @ v1_tops_1 ) ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_borsuk_1 ) )
& ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k21_borsuk_1) ).
thf(3056,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_borsuk_1 ) )
& ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(5183,plain,
! [A: $i] : ( A @ k2_pcomps_1 @ v2_pre_topc ),
inference(cnfConj,[status(thm)],[5181]) ).
thf(5184,plain,
! [A: $i] : ( A @ k2_pcomps_1 @ v2_pre_topc ),
inference(simp,[status(thm)],[5183]) ).
thf(493,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_borsuk_1) ).
thf(3593,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(325,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tsp_2) ).
thf(2865,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(5832,plain,
sk330 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5828]) ).
thf(327,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_borsuk_1) ).
thf(2875,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(5771,plain,
~ ( sk328 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5769]) ).
thf(4639,plain,
~ ( sk264 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4632]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(3284,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(384,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_tops_3) ).
thf(3139,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ v1_tops_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(899,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( B @ l1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_tsp_1) ).
thf(5981,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
=> ( B @ l1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(2479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(6943,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
!= ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ $true
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( sk329 != sk1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[6486,6905]) ).
thf(6944,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
!= ( sk1 @ ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) )
| ( sk1 @ ( B @ v3_pre_topc ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( sk329 != sk1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[6943]) ).
thf(6958,plain,
! [B: $i,A: $i] :
( ( sk1 != sk1 )
| ( ( A @ ( sk1 @ k1_struct_0 ) )
!= ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( sk329 != sk1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ ( B @ v3_pre_topc ) ) ),
inference(simp,[status(thm)],[6944]) ).
thf(6965,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ k1_struct_0 ) )
!= ( B @ ( sk1 @ u1_struct_0 @ k3_subset_1 ) ) )
| ~ ( sk1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( sk329 != sk1 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ ( B @ v3_pre_topc ) ) ),
inference(simp,[status(thm)],[6958]) ).
thf(652,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc21_tex_3) ).
thf(4606,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(172,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( C @ ( A @ k7_tex_4 ) @ ( B @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_tex_4) ).
thf(2045,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( C @ ( A @ k7_tex_4 ) @ ( B @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(42,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k1_tops_1 ) )
= C )
=> ( A @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( D @ v3_pre_topc ) )
=> ( ( D @ ( B @ k1_tops_1 ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
thf(1180,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k1_tops_1 ) )
= C )
=> ( A @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( D @ v3_pre_topc ) )
=> ( ( D @ ( B @ k1_tops_1 ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(815,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tex_3) ).
thf(5653,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2885,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(4873,plain,
~ ( k22_borsuk_1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4872]) ).
thf(180,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_tops_1) ).
thf(2078,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(297,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( A @ ( C @ v1_tex_4 ) ) )
=> ( C
= ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tex_4) ).
thf(2743,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ r1_tarski ) )
& ( A @ ( C @ v1_tex_4 ) ) )
=> ( C
= ( B @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(3346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(187,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_tops_1) ).
thf(2110,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(76,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ k1_lopclset @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lopclset) ).
thf(1390,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ k1_lopclset @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(737,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc38_tex_2) ).
thf(5124,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(120,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_tsp_1) ).
thf(1646,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) )
= ( D @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(323,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( C @ v3_tex_2 ) )
<=> ( B @ v1_tdlat_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_tex_2) ).
thf(2855,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( B @ v1_tdlat_3 )
=> ( A @ ( C @ v3_tex_2 ) ) )
& ( ( A @ ( C @ v3_tex_2 ) )
=> ( B @ v1_tdlat_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(580,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc25_tex_3) ).
thf(4089,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( A @ ( B @ m2_tsp_1 ) )
<=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ v4_pre_topc ) )
<=> ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tsp_1) ).
thf(2532,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v4_pre_topc ) ) )
& ( ( B @ ( C @ v4_pre_topc ) )
=> ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
=> ( A @ ( B @ m2_tsp_1 ) ) )
& ( ( A @ ( B @ m2_tsp_1 ) )
=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v4_pre_topc ) ) )
& ( ( B @ ( C @ v4_pre_topc ) )
=> ? [D: $i] :
( ( C
= ( B @ u1_struct_0 @ ( D @ k3_xboole_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(600,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lopclset) ).
thf(4250,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(784,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_tdlat_3) ).
thf(5426,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(526,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( A @ ( B @ v2_tex_2 ) ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tex_2) ).
thf(3748,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( A @ ( B @ v2_tex_2 ) ) )
=> ( ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) )
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(6003,plain,
sk338 @ v2_t_0topsp,
inference(cnfConj,[status(thm)],[6001]) ).
thf(6906,plain,
( ( ( sk338 @ v2_t_0topsp )
!= ( sk238 @ v2_t_0topsp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6003,4220]) ).
thf(6907,plain,
( ( sk338 @ v2_t_0topsp )
!= ( sk238 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[6906]) ).
thf(6910,plain,
sk338 != sk238,
inference(simp,[status(thm)],[6907]) ).
thf(485,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_tsp_1) ).
thf(3561,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tsp_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(4527,plain,
sk255 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[4520]) ).
thf(12525,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ $true
| ( sk2 @ v2_t_0topsp ) ),
inference(paramod_ordered,[status(thm)],[12516,6483]) ).
thf(12526,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk6 ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( sk1 @ ( A @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk2 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[12525]) ).
thf(12527,plain,
( ( sk1 @ ( sk1 @ ( sk2 @ sk6 ) @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk2 @ v2_t_0topsp ) ),
inference(pattern_uni,[status(thm)],[12526:[bind(A,$thf( sk1 @ ( sk2 @ sk6 ) ))]]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v3_realset2 )
& ( B @ ( A @ k1_tex_2 ) @ v5_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v4_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v3_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v1_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_pre_topc )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tex_2) ).
thf(5055,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v3_realset2 )
& ( B @ ( A @ k1_tex_2 ) @ v5_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v4_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v3_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v1_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_pre_topc )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(961,plain,
! [B: $i,A: $i] :
( ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(277,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ~ ( A @ ( B @ v4_tex_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_tex_2) ).
thf(2594,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ~ ( A @ ( B @ v4_tex_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_tsp_2 ) )
= ( B @ ( A @ k1_tsp_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_tsp_2) ).
thf(5724,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_tsp_2 ) )
= ( B @ ( A @ k1_tsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( D @ ( B @ k6_pre_topc ) )
= ( B @ k2_pre_topc @ ( C @ ( A @ k6_pre_topc ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_pre_topc) ).
thf(2283,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( D @ ( B @ k6_pre_topc ) )
= ( B @ k2_pre_topc @ ( C @ ( A @ k6_pre_topc ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_3 ) )
<=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tops_3) ).
thf(1903,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) )
=> ( A @ ( B @ v1_tops_3 ) ) )
& ( ( A @ ( B @ v1_tops_3 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(661,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc19_tex_2) ).
thf(4666,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(663,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v3_tdlat_3 )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v3_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_tex_2) ).
thf(4683,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v3_tdlat_3 )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v3_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(442,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v4_tex_4 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
& ( C @ v2_tdlat_3 ) )
=> ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) ) ) )
& ( B @ v2_tdlat_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_tex_4) ).
thf(3383,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
& ( C @ v2_tdlat_3 ) )
=> ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) ) ) )
& ( B @ v2_tdlat_3 ) )
=> ( A @ ( B @ v4_tex_4 ) ) )
& ( ( A @ ( B @ v4_tex_4 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
& ( C @ v2_tdlat_3 ) )
=> ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) ) ) )
& ( B @ v2_tdlat_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(439,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_tops_3) ).
thf(3369,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(571,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
=> ( ( A @ ( B @ v3_tex_3 ) )
<=> ( A @ ( C @ v1_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_tex_3) ).
thf(4042,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
=> ( ( ( A @ ( C @ v1_tex_3 ) )
=> ( A @ ( B @ v3_tex_3 ) ) )
& ( ( A @ ( B @ v3_tex_3 ) )
=> ( A @ ( C @ v1_tex_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(9654,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2920,3668]) ).
thf(9655,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( B @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9654]) ).
thf(9662,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk175 )
!= B )
| ~ ( B @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9655]) ).
thf(9679,plain,
! [A: $i] :
( ( ( A @ sk175 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ~ ( A @ sk175 @ k1_zfmisc_1 @ ( A @ sk175 @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9662]) ).
thf(22025,plain,
! [A: $i] :
( ( ( A @ sk175 )
!= A )
| ~ ( A @ sk175 @ k1_zfmisc_1 @ ( A @ sk175 @ v1_tex_2 ) ) ),
inference(simp,[status(thm)],[9679]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(1629,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(912,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m2_tsp_1 ) )
<=> ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_tsp_1) ).
thf(6023,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ ( B @ m2_tsp_1 ) ) )
& ( ( A @ ( B @ m2_tsp_1 ) )
=> ( A @ ( B @ m1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(848,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k3_tdlat_1 )
= ( A @ k11_tdlat_1 ) )
& ( ( A @ k2_tdlat_1 )
= ( A @ k10_tdlat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_tdlat_3) ).
thf(5813,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k3_tdlat_1 )
= ( A @ k11_tdlat_1 ) )
& ( ( A @ k2_tdlat_1 )
= ( A @ k10_tdlat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(638,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_pre_topc) ).
thf(4495,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(545,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v3_realset2 )
& ( B @ ( A @ k1_tex_2 ) @ v5_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v4_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v3_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v1_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_pre_topc )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_tex_2) ).
thf(3859,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v3_realset2 )
& ( B @ ( A @ k1_tex_2 ) @ v5_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v4_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v3_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v1_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v2_pre_topc )
& ( B @ ( A @ k1_tex_2 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k1_tex_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(3136,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(412,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_tops_3) ).
thf(3252,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(798,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc47_tex_2) ).
thf(5505,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(711,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc27_tex_3) ).
thf(4969,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
=> ( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(101,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v1_tex_4 ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v1_tex_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tex_4) ).
thf(1558,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v1_tex_4 ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( A @ ( C @ v1_tex_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(197,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( C @ v1_tops_1 ) ) )
<=> ( A @ ( D @ v1_tops_3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_tops_3) ).
thf(2152,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( ( ( A @ ( D @ v1_tops_3 ) )
=> ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( C @ v1_tops_1 ) ) ) )
& ( ( ( B @ ( E @ v1_tops_3 ) )
& ( A @ ( C @ v1_tops_1 ) ) )
=> ( A @ ( D @ v1_tops_3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ( B @ ( C @ ( A @ r4_tsep_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r4_tsep_1) ).
thf(3978,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ( B @ ( C @ ( A @ r4_tsep_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(514,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_tops_3) ).
thf(3694,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_3 ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(430,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v3_tex_3 ) ) ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tex_3) ).
thf(3324,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ~ ( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ v3_tex_3 ) ) ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(743,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v1_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_tex_3) ).
thf(5164,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( ( A @ v1_tdlat_3 )
& ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(3676,plain,
! [A: $i] :
( ( ~ ( A @ sk212 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk212 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3675]) ).
thf(3677,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ sk212 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3676]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_tops_1) ).
thf(1607,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(5739,plain,
~ ( sk324 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5738]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(2902,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( A @ ( D @ v2_tops_1 ) )
& ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( B @ ( E @ v2_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_tops_3) ).
thf(1309,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( A @ ( D @ v2_tops_1 ) )
& ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( B @ ( E @ v2_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(823,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( E @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( A @ ( E @ m1_pre_topc ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_tsep_1) ).
thf(5704,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( E @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( A @ ( E @ m1_pre_topc ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( D @ ( A @ k2_tsep_1 ) ) @ ( A @ r1_tsep_1 ) ) )
| ( E @ ( D @ ( A @ r1_tsep_1 ) ) ) )
& ( E @ ( C @ m1_pre_topc ) )
& ( D @ ( B @ m1_pre_topc ) )
& ( E @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( A @ ( E @ m1_pre_topc ) )
& ~ ( E @ v3_struct_0 ) )
& ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(569,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( C
= ( B @ ( A @ k6_borsuk_1 ) ) )
<=> ( ( ( C @ u1_pre_topc )
= ( C @ ( B @ ( A @ a_3_0_borsuk_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_borsuk_1) ).
thf(4025,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( ( ( ( C @ u1_pre_topc )
= ( C @ ( B @ ( A @ a_3_0_borsuk_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) ) ) )
=> ( C
= ( B @ ( A @ k6_borsuk_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k6_borsuk_1 ) ) )
=> ( ( ( C @ u1_pre_topc )
= ( C @ ( B @ ( A @ a_3_0_borsuk_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(252,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r1_xboole_0 ) )
& ( E @ ( C @ r1_tarski ) )
& ( D @ ( B @ r1_tarski ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ~ ( ( F @ ( E @ r1_xboole_0 ) )
& ( F @ ( D @ r2_hidden ) )
& ( E @ ( B @ r1_tarski ) )
& ( A @ ( F @ v3_pre_topc ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) )
& ( C @ ( D @ r2_hidden ) ) ) )
& ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ v2_pcomps_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_pcomps_1) ).
thf(2421,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r1_xboole_0 ) )
& ( E @ ( C @ r1_tarski ) )
& ( D @ ( B @ r1_tarski ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ~ ( ( F @ ( E @ r1_xboole_0 ) )
& ( F @ ( D @ r2_hidden ) )
& ( E @ ( B @ r1_tarski ) )
& ( A @ ( F @ v3_pre_topc ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) )
& ( C @ ( D @ r2_hidden ) ) ) )
& ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ v2_pcomps_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( C @ v4_tex_2 ) )
<=> ( A @ ( B @ v5_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tex_2) ).
thf(1030,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( B @ v5_tex_2 ) )
=> ( A @ ( C @ v4_tex_2 ) ) )
& ( ( A @ ( C @ v4_tex_2 ) )
=> ( A @ ( B @ v5_tex_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(892,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_tsp_2) ).
thf(5963,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v2_tsp_2 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(6043,plain,
( ( ( sk264 @ v2_t_0topsp )
!= ( sk238 @ v2_t_0topsp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4636,4220]) ).
thf(6044,plain,
( ( sk264 @ v2_t_0topsp )
!= ( sk238 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[6043]) ).
thf(6045,plain,
sk264 != sk238,
inference(simp,[status(thm)],[6044]) ).
thf(495,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ a_3_1_pcomps_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pcomps_1) ).
thf(3598,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ a_3_1_pcomps_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_tsp_2 ) )
= ( B @ ( A @ k1_tsp_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_tsp_2) ).
thf(5837,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v2_tsp_2 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_tsp_2 ) )
= ( B @ ( A @ k1_tsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r1_tarski ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[928]) ).
thf(551,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v2_tdlat_3 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_tex_4) ).
thf(3896,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v2_tdlat_3 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) ) )
=> ( ( C @ ( B @ m1_pre_topc ) )
| ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k7_tex_4 ) @ m1_pre_topc ) )
& ( B @ ( A @ k7_tex_4 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_tex_4) ).
thf(2198,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k7_tex_4 ) @ m1_pre_topc ) )
& ( B @ ( A @ k7_tex_4 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(738,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( D @ ( C @ ( A @ r3_tsep_1 ) ) )
& ( D @ ( B @ ( A @ r3_tsep_1 ) ) ) )
<=> ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_tsep_1) ).
thf(5128,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) )
=> ( ( D @ ( C @ ( A @ r3_tsep_1 ) ) )
& ( D @ ( B @ ( A @ r3_tsep_1 ) ) ) ) )
& ( ( ( D @ ( C @ ( A @ r3_tsep_1 ) ) )
& ( D @ ( B @ ( A @ r3_tsep_1 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(229,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_tex_2) ).
thf(2315,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( A @ k1_struct_0 ) ) )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(264,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k4_t_0topsp @ ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( A @ k4_t_0topsp @ ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_t_0topsp) ).
thf(2494,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k4_t_0topsp @ ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( A @ k4_t_0topsp @ ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(646,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v4_tex_3 ) )
<=> ? [C: $i] :
( ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_tex_3) ).
thf(4570,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( A @ ( B @ v4_tex_3 ) ) )
& ( ( A @ ( B @ v4_tex_3 ) )
=> ? [C: $i] :
( ( C @ ( B @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_borsuk_1) ).
thf(4372,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(2623,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(529,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v5_tdlat_3 )
<=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ v4_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tdlat_3) ).
thf(3761,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ v4_tdlat_3 ) )
=> ( A @ v5_tdlat_3 ) )
& ( ( A @ v5_tdlat_3 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ v4_tdlat_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(8888,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ $true
| ~ ( A @ l1_pre_topc ) ),
inference(paramod_ordered,[status(thm)],[918,961]) ).
thf(8889,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ( B @ u1_struct_0 @ ( A @ ( B @ sk5 ) @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[8888]) ).
thf(8890,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk2 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
| ~ ( sk1 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[8889:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(9838,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk2 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8890,922]) ).
thf(9839,plain,
( ( sk2 @ v2_t_0topsp )
| ( sk2 @ u1_struct_0 @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[9838]) ).
thf(860,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m2_tsp_1 ) )
=> ( B @ v2_t_0topsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tsp_1) ).
thf(5864,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_tsp_1 ) )
& ( C @ v2_t_0topsp )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ m2_tsp_1 ) )
=> ( B @ v2_t_0topsp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tex_4 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v1_tex_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tex_4) ).
thf(1348,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tex_4 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v1_tex_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(223,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
thf(2287,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(680,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_tex_3) ).
thf(4794,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(129,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(1725,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ v3_tsp_1 ) )
<=> ( B @ v2_t_0topsp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v3_tsp_1) ).
thf(4809,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ l1_pre_topc ) )
=> ( ( ( B @ v2_t_0topsp )
=> ( A @ ( B @ v3_tsp_1 ) ) )
& ( ( A @ ( B @ v3_tsp_1 ) )
=> ( B @ v2_t_0topsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(758,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) @ k2_relat_1 )
= ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_borsuk_1) ).
thf(5268,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) @ k2_relat_1 )
= ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(785,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_tex_3) ).
thf(5430,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(465,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_tops_3) ).
thf(3464,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ v1_tops_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(8488,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ~ $true
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(paramod_ordered,[status(thm)],[2920,6486]) ).
thf(8489,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8488]) ).
thf(8550,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( A @ sk175 )
!= B )
| ( sk329 != sk1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8489]) ).
thf(8574,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( sk329 != sk1 )
| ( sk1 @ ( A @ sk175 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8550]) ).
thf(617,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_tex_2) ).
thf(4357,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( B @ v3_struct_0 )
=> ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(5760,plain,
~ ( sk327 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5758]) ).
thf(404,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(3203,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(6053,plain,
( ( ( sk290 @ v1_tdlat_3 )
!= ( sk255 @ v1_tdlat_3 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4524,5253]) ).
thf(6054,plain,
( ( sk290 @ v1_tdlat_3 )
!= ( sk255 @ v1_tdlat_3 ) ),
inference(simp,[status(thm)],[6053]) ).
thf(6055,plain,
sk290 != sk255,
inference(simp,[status(thm)],[6054]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( A @ ( C @ v4_pre_topc ) )
<=> ( B @ ( D @ v4_pre_topc ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_tops_3) ).
thf(1578,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( B @ ( D @ v4_pre_topc ) )
=> ( A @ ( C @ v4_pre_topc ) ) )
& ( ( A @ ( C @ v4_pre_topc ) )
=> ( B @ ( D @ v4_pre_topc ) ) ) ) ) ) )
& ( ( A @ u1_struct_0 )
= ( B @ u1_struct_0 ) ) )
=> ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(634,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
<=> ? [C: $i] :
( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_tex_3) ).
thf(4472,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ? [C: $i] :
( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) )
=> ( A @ ( B @ v2_tex_3 ) ) )
& ( ( A @ ( B @ v2_tex_3 ) )
=> ? [C: $i] :
( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(243,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( A @ ( C @ v4_tex_2 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( A @ ( B @ v3_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_tex_2) ).
thf(2385,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( A @ ( C @ v4_tex_2 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( A @ ( B @ v3_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(533,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v3_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc28_tex_3) ).
thf(3785,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v3_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(894,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_tex_2) ).
thf(5971,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( B @ v1_tdlat_3 )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ ( A @ r1_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(906,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k4_t_0topsp )
= ( A @ k2_t_0topsp @ ( A @ k17_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_t_0topsp) ).
thf(6007,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k4_t_0topsp )
= ( A @ k2_t_0topsp @ ( A @ k17_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(566,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(3997,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(843,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_pre_topc @ v3_tops_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_tops_3) ).
thf(5796,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_pre_topc @ v3_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(416,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( A @ ( B @ v2_borsuk_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_borsuk_1) ).
thf(3264,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) )
=> ( A @ ( B @ v2_borsuk_1 ) ) )
& ( ( A @ ( B @ v2_borsuk_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(803,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_tex_3) ).
thf(5537,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v3_tex_3 ) )
& ( A @ ( C @ v1_borsuk_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(728,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ~ ( D @ ( C @ ( A @ r1_tsep_1 ) ) )
=> ( ( ( ( D @ ( B @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
=> ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( ( B @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( B @ ( C @ ( A @ r4_tsep_1 ) ) ) )
=> ( B @ ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_tsep_1) ).
thf(5078,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ~ ( D @ v3_struct_0 ) )
=> ( ~ ( D @ ( C @ ( A @ r1_tsep_1 ) ) )
=> ( ( ( ( D @ ( B @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
=> ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( ( B @ ( D @ ( A @ r4_tsep_1 ) ) )
& ( B @ ( C @ ( A @ r4_tsep_1 ) ) ) )
=> ( B @ ( D @ ( C @ ( A @ k2_tsep_1 ) ) @ ( A @ r4_tsep_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(4523,plain,
sk255 @ v3_tdlat_3,
inference(cnfConj,[status(thm)],[4520]) ).
thf(690,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_realset2 )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_tex_2) ).
thf(4841,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_realset2 )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(168,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k2_t_0topsp @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ r1_tarski ) )
| ( B @ ( C @ r1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_t_0topsp) ).
thf(1986,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k2_t_0topsp @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ r1_tarski ) )
| ( B @ ( C @ r1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(647,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_tsep_1) ).
thf(4579,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_tsep_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tsep_1 ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(9904,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[4488,9839]) ).
thf(9944,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 )
!= sk2 )
| ( sk2 @ v2_t_0topsp )
| ( A @ ( sk1 @ ( sk2 @ sk5 ) @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[9904]) ).
thf(355,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v2_pre_topc )
=> ( ( B @ ( A @ k1_tex_2 ) @ v2_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v1_tdlat_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_tex_2) ).
thf(3015,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tex_2 ) @ v2_pre_topc )
=> ( ( B @ ( A @ k1_tex_2 ) @ v2_tdlat_3 )
& ( B @ ( A @ k1_tex_2 ) @ v1_tdlat_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(763,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc30_tex_3) ).
thf(5300,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(146,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( C @ v1_tsp_1 ) )
<=> ( B @ v2_t_0topsp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_tsp_1) ).
thf(1816,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_tsp_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( B @ v2_t_0topsp )
=> ( A @ ( C @ v1_tsp_1 ) ) )
& ( ( A @ ( C @ v1_tsp_1 ) )
=> ( B @ v2_t_0topsp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(8201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk179 @ v1_xboole_0 )
!= ( C @ v1_xboole_0 ) )
| ~ $true
| ~ ( C @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[2997,2789]) ).
thf(8202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk179 @ v1_xboole_0 )
!= ( C @ v1_xboole_0 ) )
| ~ ( C @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[8201]) ).
thf(8203,plain,
! [B: $i,A: $i] :
~ ( B @ sk179 @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[8202:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ sk179 ))]]) ).
thf(8207,plain,
! [B: $i,A: $i] :
~ ( B @ sk179 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[8203]) ).
thf(203,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_3) ).
thf(2186,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(2746,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(520,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
<=> ( ( B @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_tex_4) ).
thf(3716,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( ( B @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) )
& ( ( ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) )
= ( C @ ( A @ k7_tex_4 ) @ u1_pre_topc @ ( C @ ( A @ k7_tex_4 ) @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(292,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tex_2 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v3_tex_2 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v3_tex_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_tex_2) ).
thf(2704,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v3_tex_2 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v3_tex_2 ) ) )
=> ( A @ ( B @ v4_tex_2 ) ) )
& ( ( A @ ( B @ v4_tex_2 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ v3_tex_2 ) ) )
=> ( B = C ) ) )
& ( A @ ( B @ v3_tex_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(60,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_tex_4) ).
thf(1288,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_tex_4 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(591,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v1_tdlat_3 )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v1_tdlat_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tex_2) ).
thf(4193,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( A @ v1_tdlat_3 )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ v1_tdlat_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(543,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_tex_3) ).
thf(3843,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v4_tex_3 ) )
& ~ ( A @ ( B @ v3_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(786,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc26_tex_3) ).
thf(5440,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_tex_4 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc16_tex_4) ).
thf(2783,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_tex_4 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_tex_4 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(805,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v3_tex_3 ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ~ ( ( ( D @ ( C @ ( A @ k1_tsep_1 ) ) )
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) )
& ( ( D @ ( C @ ( A @ k2_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) )
& ~ ( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v3_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_tex_3) ).
thf(5559,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v4_tex_3 ) )
& ~ ( B @ v3_struct_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( C @ v2_tex_2 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v3_tex_3 ) )
& ( A @ ( D @ v1_borsuk_1 ) )
& ( D @ v1_pre_topc )
& ~ ( D @ v3_struct_0 ) )
=> ~ ( ( ( D @ ( C @ ( A @ k1_tsep_1 ) ) )
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) )
& ( ( D @ ( C @ ( A @ k2_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) )
& ~ ( ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v3_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(3145,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(5741,plain,
sk324 @ v5_tdlat_3,
inference(cnfConj,[status(thm)],[5738]) ).
thf(251,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tsp_2 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tsp_2) ).
thf(2417,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_tsp_2 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(293,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
<=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tsep_1) ).
thf(2714,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
=> ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) ) )
& ( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(450,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_tex_4) ).
thf(3426,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( A @ k7_tex_4 ) @ m1_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(5251,plain,
~ ( sk290 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5248]) ).
thf(357,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
<=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tex_3) ).
thf(3030,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
=> ( A @ ( B @ v1_tex_3 ) ) )
& ( ( A @ ( B @ v1_tex_3 ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(57896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ( E @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[12351,3104]) ).
thf(57897,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( B @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[57896:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ k2_xboole_0 ) )),bind(D,$thf( F ))]]) ).
thf(58061,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( B @ r1_tarski ) ),
inference(simp,[status(thm)],[57897]) ).
thf(91,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
thf(1473,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(508,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v6_compts_1 ) )
& ( A @ v3_compts_1 ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_compts_1) ).
thf(3673,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v6_compts_1 ) )
& ( A @ v3_compts_1 ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(761,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_tex_3) ).
thf(5283,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_tex_3 ) )
& ( A @ ( B @ v3_tex_3 ) )
& ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ~ ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(177,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( D @ ( A @ k1_struct_0 ) ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_tex_2) ).
thf(2063,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( D @ ( A @ k1_struct_0 ) ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) )
& ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( A @ k1_struct_0 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( D @ ( A @ k1_struct_0 ) ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(111,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v1_tsp_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_tsp_1) ).
thf(1610,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v1_tsp_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(610,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) ) )
| ( ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_tex_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_tex_3) ).
thf(4318,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( ( A @ ( C @ v2_tex_3 ) )
& ( A @ ( B @ v1_tex_3 ) ) )
| ( ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( B @ v2_tex_3 ) ) ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( A @ ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ v1_tex_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(132,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( D
= ( E @ ( A @ k1_struct_0 ) ) )
& ~ ( B @ k2_pre_topc @ ( E @ r2_hidden ) ) ) )
& ~ ( C @ ( D @ r2_hidden ) )
& ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_borsuk_1) ).
thf(1742,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( D
= ( E @ ( A @ k1_struct_0 ) ) )
& ~ ( B @ k2_pre_topc @ ( E @ r2_hidden ) ) ) )
& ~ ( C @ ( D @ r2_hidden ) )
& ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).
thf(2353,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(1352,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_tops_1) ).
thf(1129,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(46440,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ~ $true
| ~ ( A @ l1_pre_topc )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[918,988]) ).
thf(46441,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m2_tsp_1 ) )
!= ( A @ ( B @ m2_tsp_1 ) ) )
| ( B @ v2_t_0topsp )
| ~ ( A @ l1_pre_topc )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) ) ),
inference(simp,[status(thm)],[46440]) ).
thf(46442,plain,
( ( sk2 @ v2_t_0topsp )
| ~ ( sk1 @ l1_pre_topc )
| ( ( sk1 @ ( sk2 @ sk6 ) )
!= ( sk1 @ ( sk2 @ sk5 ) ) ) ),
inference(pattern_uni,[status(thm)],[46441:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(46923,plain,
( ( sk2 @ v2_t_0topsp )
| ~ $true
| ( ( sk1 @ ( sk2 @ sk6 ) )
!= ( sk1 @ ( sk2 @ sk5 ) ) ) ),
inference(rewrite,[status(thm)],[46442,922]) ).
thf(46924,plain,
( ( sk2 @ v2_t_0topsp )
| ( ( sk1 @ ( sk2 @ sk6 ) )
!= ( sk1 @ ( sk2 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[46923]) ).
thf(577,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v5_tex_2 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tex_3) ).
thf(4066,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_realset2 )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( A @ ( B @ v2_tex_3 ) )
& ~ ( A @ ( B @ v1_tex_3 ) )
& ~ ( A @ ( B @ v5_tex_2 ) )
& ( A @ ( B @ v2_tex_2 ) )
& ( B @ v3_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_tsep_1 ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ v3_pre_topc ) )
| ( A @ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ v3_pre_topc ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[967]) ).
thf(8640,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ~ $true
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(paramod_ordered,[status(thm)],[2996,6486]) ).
thf(8641,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk179 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk329 != sk1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8640]) ).
thf(8696,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( A @ sk179 )
!= B )
| ( sk329 != sk1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8641]) ).
thf(8730,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( sk329 != sk1 )
| ( sk1 @ ( A @ sk179 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8696]) ).
thf(689,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( B @ ( C @ m1_pre_topc ) ) )
& ( ( B @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( C @ ( B @ m1_pre_topc ) ) )
& ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_tsep_1) ).
thf(4831,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( B @ ( C @ m1_pre_topc ) ) )
& ( ( B @ ( C @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( C @ u1_pre_topc @ ( C @ u1_struct_0 @ g1_pre_topc ) ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) )
=> ( C @ ( B @ m1_pre_topc ) ) )
& ( ( C @ ( B @ m1_pre_topc ) )
=> ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(723,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_tex_2) ).
thf(5046,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v2_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(771,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
=> ( ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( B @ v2_tex_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tex_3) ).
thf(5354,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_2 ) ) )
=> ( ( A @ ( C @ v2_tex_2 ) )
& ( A @ ( B @ v2_tex_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(6908,plain,
( ( ( sk338 @ v2_t_0topsp )
!= ( sk290 @ v2_t_0topsp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6003,5255]) ).
thf(6909,plain,
( ( sk338 @ v2_t_0topsp )
!= ( sk290 @ v2_t_0topsp ) ),
inference(simp,[status(thm)],[6908]) ).
thf(6911,plain,
sk338 != sk290,
inference(simp,[status(thm)],[6909]) ).
thf(15286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
!= ( C @ ( D @ k2_xboole_0 ) ) )
| ~ ( C @ ( A @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3473,15252]) ).
thf(15287,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ k2_xboole_0 ) @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[15286:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(2270,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(4221,plain,
~ ( sk238 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4215]) ).
thf(215,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ v3_tdlat_3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_tdlat_3) ).
thf(2241,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) )
=> ( A @ v3_tdlat_3 ) )
& ( ( A @ v3_tdlat_3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( D @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[965]) ).
thf(691,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc46_tex_2) ).
thf(4848,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( A @ ( B @ v5_tex_2 ) )
& ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ( B @ v2_tdlat_3 )
& ~ ( B @ v1_tdlat_3 )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(8323,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( sk1 @ ( A @ sk174 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 ) ),
inference(paramod_ordered,[status(thm)],[4488,8063]) ).
thf(8328,plain,
! [A: $i] :
( ( ( A @ k2_pcomps_1 )
!= sk1 )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( A @ sk174 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8323]) ).
thf(598,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ k2_t_0topsp @ m1_eqrel_1 ) )
& ~ ( A @ k2_t_0topsp @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_t_0topsp) ).
thf(4242,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ k2_t_0topsp @ m1_eqrel_1 ) )
& ~ ( A @ k2_t_0topsp @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(694,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tsp_1) ).
thf(4876,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( A @ v2_t_0topsp )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ~ ( A @ v2_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(896,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) ) )
=> ( A @ ( C @ v3_tex_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_tex_3) ).
thf(5975,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pre_topc ) )
=> ( ( ( B @ ( C @ m1_pre_topc ) )
& ( A @ ( B @ v3_tex_3 ) ) )
=> ( A @ ( C @ v3_tex_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(99,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_pre_topc ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_tsep_1) ).
thf(1550,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_pre_topc ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ r1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(4229,plain,
sk239 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[4228]) ).
thf(969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ( C = D )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[954]) ).
thf(982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( C @ r2_hidden ) )
| ( A @ ( B @ ( C @ ( D @ sk3 ) ) ) @ ( C @ r2_hidden ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( B @ v3_struct_0 )
| ~ ( B @ v2_t_0topsp )
| ~ ( A @ ( B @ m2_tsp_1 ) )
| ~ ( A @ l1_pre_topc )
| ( C = D ) ),
inference(lifteq,[status(thm)],[969]) ).
thf(15,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_tops_3) ).
thf(1004,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v2_tops_1 ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8447,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2920,6483]) ).
thf(8448,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk175 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) )
| ~ ( sk1 @ v3_compts_1 ) ),
inference(simp,[status(thm)],[8447]) ).
thf(8545,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( A @ sk175 )
!= B )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( B @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8448]) ).
thf(8570,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 )
!= ( sk1 @ u1_struct_0 ) )
| ~ ( sk1 @ v3_compts_1 )
| ( sk1 @ ( A @ sk175 @ ( sk1 @ k1_struct_0 ) @ v4_pre_topc ) ) ),
inference(simp,[status(thm)],[8545]) ).
thf(768,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tex_3) ).
thf(5344,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ~ ( A @ ( B @ v2_tex_3 ) )
=> ( ( A @ ( B @ v2_tex_2 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(433,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ u1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(3341,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ u1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(3474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(478,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v1_tops_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_tops_3) ).
thf(3528,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v1_tops_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(807,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) )
<=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_tsep_1) ).
thf(5591,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_tsep_1 ) ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
& ( C @ ( B @ ( A @ r1_tsep_1 ) ) ) )
=> ( C @ ( B @ ( A @ r3_tsep_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(30828,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) )
!= ( D @ ( C @ k3_xboole_0 ) ) )
| ~ ( D @ ( C @ r1_xboole_0 ) )
| ~ ( A @ ( B @ k3_xboole_0 ) @ ( E @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[3296,1557]) ).
thf(30829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ~ ( A @ ( B @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[30828:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(30854,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ~ ( A @ ( B @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30829]) ).
thf(351,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tsep_1) ).
thf(2998,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( B
= ( C @ u1_struct_0 ) )
& ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(319,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k4_t_0topsp @ ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_t_0topsp) ).
thf(2832,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k4_t_0topsp @ ( A @ k3_t_0topsp @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k6_pre_topc ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_pre_topc) ).
thf(1416,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k6_pre_topc ) ) ) )
& ( ( C
= ( B @ ( A @ k6_pre_topc ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(3432,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(354,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_lopclset @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lopclset) ).
thf(3013,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_lopclset @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(560,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ~ ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc32_tex_2) ).
thf(3960,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v1_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ~ ( B @ v3_realset2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ~ ( B @ v3_realset2 )
& ( B @ v5_tdlat_3 )
& ( B @ v4_tdlat_3 )
& ( B @ v3_tdlat_3 )
& ~ ( B @ v2_tdlat_3 )
& ( B @ v1_tdlat_3 )
& ( A @ ( B @ v1_borsuk_1 ) )
& ( A @ ( B @ v1_tsep_1 ) )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(454,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v6_compts_1 ) )
& ( A @ ( B @ v6_compts_1 ) )
& ( A @ v3_compts_1 ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v6_compts_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_compts_1) ).
thf(3437,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v6_compts_1 ) )
& ( A @ ( B @ v6_compts_1 ) )
& ( A @ v3_compts_1 ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v6_compts_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(720,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tex_3) ).
thf(5029,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
=> ( ( A @ ( B @ v1_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(2321,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(556,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
<=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_borsuk_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( F @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ~ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) ) )
& ( C @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_tsep_1) ).
thf(3924,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 ) )
=> ( ~ ( C @ ( B @ ( A @ r1_tsep_1 ) ) )
=> ( ( ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_borsuk_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( F @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ~ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) ) )
& ( C @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) )
=> ( C @ ( B @ ( A @ r4_tsep_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_tsep_1 ) ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_pre_topc ) )
& ( A @ ( D @ v1_tsep_1 ) )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_pre_topc ) )
& ( A @ ( E @ v1_tsep_1 ) )
& ~ ( E @ v3_struct_0 ) )
=> ~ ( ~ ( ! [F: $i] :
( ( ( A @ ( F @ m1_pre_topc ) )
& ( A @ ( F @ v1_borsuk_1 ) )
& ~ ( F @ v3_struct_0 ) )
=> ~ ( ( C @ ( B @ ( A @ k2_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( F @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( F @ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( A @ k1_tsep_1 ) ) ) ) ) )
& ~ ( E @ ( D @ ( A @ k1_tsep_1 ) ) @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ m1_pre_topc ) ) )
& ( C @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( E @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) )
& ( B @ ( C @ ( B @ ( A @ k1_tsep_1 ) ) @ ( D @ ( A @ k2_tsep_1 ) ) @ m1_pre_topc ) ) ) ) )
& ~ ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ ( B @ m1_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(5986,plain,
~ ( sk337 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5984]) ).
thf(923,plain,
sk1 @ ( sk2 @ v2_tsp_2 ),
inference(cnfConj,[status(thm)],[917]) ).
thf(5789,plain,
sk329 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5784]) ).
thf(678,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_borsuk_1) ).
thf(4784,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(178,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_tops_3) ).
thf(2074,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( B @ v1_tops_3 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_tops_1) ).
thf(2436,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(154,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_tsp_1) ).
thf(1848,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
=> ( A @ ( B @ v1_tsp_1 ) ) )
& ( ( A @ ( B @ v1_tsp_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( D @ r2_hidden ) )
& ~ ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ~ ( E @ ( D @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( A @ ( E @ v4_pre_topc ) ) ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tsp_1 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v1_tsp_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tsp_1) ).
thf(2059,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tsp_1 ) )
& ( C = D )
& ( ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) )
= ( B @ u1_pre_topc @ ( B @ u1_struct_0 @ g1_pre_topc ) ) ) )
=> ( B @ ( D @ v1_tsp_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(255,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_tops_1) ).
thf(2438,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(457,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_borsuk_1) ).
thf(3443,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(787,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_pcomps_1 @ v2_pre_topc )
& ( A @ k2_pcomps_1 @ v1_pre_topc )
& ~ ( A @ k2_pcomps_1 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pcomps_1) ).
thf(5445,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_pcomps_1 @ v2_pre_topc )
& ( A @ k2_pcomps_1 @ v1_pre_topc )
& ~ ( A @ k2_pcomps_1 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(283,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(2615,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tex_2 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B @ ( C @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_tex_2) ).
thf(1769,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B @ ( C @ r1_tarski ) ) ) )
=> ( A @ ( B @ v3_tex_2 ) ) )
& ( ( A @ ( B @ v3_tex_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= C )
& ( A @ ( D @ v4_pre_topc ) ) ) )
& ( B @ ( C @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(574,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
=> ( ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_tex_3) ).
thf(4056,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v2_tex_3 ) )
=> ( ~ ( A @ ( B @ v3_tex_3 ) )
& ( B @ v2_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(320,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_tex_3) ).
thf(2834,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( A @ ( C @ v1_tsep_1 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(5732,plain,
! [A: $i] : ( A @ k2_pcomps_1 @ l1_pre_topc ),
inference(cnf,[status(esa)],[5731]) ).
thf(915,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v2_tdlat_3 )
=> ( B @ v2_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_tex_2) ).
thf(6035,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( B @ v2_tdlat_3 )
=> ( B @ v2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(186,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v4_pre_topc ) ) )
=> ( ( D @ ( A @ k6_pre_topc ) )
= ( E @ ( B @ k6_pre_topc ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_tops_3) ).
thf(2106,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( D = E )
& ( C @ ( D @ r1_tarski ) )
& ( B @ u1_struct_0 @ ( C @ r1_tarski ) )
& ( A @ ( C @ v4_pre_topc ) ) )
=> ( ( D @ ( A @ k6_pre_topc ) )
= ( E @ ( B @ k6_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(483,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_tdlat_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_tdlat_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k3_tdlat_1 @ k1_binop_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tdlat_1 @ k1_binop_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_tdlat_3) ).
thf(3553,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_tdlat_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_tdlat_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k3_tdlat_1 @ k1_binop_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tdlat_1 @ k1_binop_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(361,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( C
= ( B @ u1_struct_0 ) ) )
=> ( B @ v4_tdlat_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_tdlat_3) ).
thf(3047,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v4_tdlat_3 )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v1_tops_1 ) )
& ( C
= ( B @ u1_struct_0 ) ) )
=> ( B @ v4_tdlat_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(704,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_tsp_1 ) )
<=> ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_tsp_1) ).
thf(4940,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ ( B @ m1_tsp_1 ) ) )
& ( ( A @ ( B @ m1_tsp_1 ) )
=> ( A @ ( B @ m1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(488,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tex_3) ).
thf(3575,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( A @ ( C @ v1_tex_3 ) )
& ( C @ v1_pre_topc )
& ~ ( C @ v3_struct_0 ) )
=> ( B
!= ( C @ u1_struct_0 ) ) )
& ( A @ ( B @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(88600,plain,
$false,
inference(e,[status(thm)],[2163,21729,5469,3883,5918,2889,5896,3661,3399,3434,5390,1840,47442,4015,4992,4904,2306,5857,3053,4101,2336,1454,1237,5320,2921,3477,2787,5676,941,9676,6042,5733,5898,2210,5225,3317,1290,2231,3040,5878,3108,2114,4326,5501,4311,1522,2644,4515,3813,2381,5644,3549,2776,1808,2659,5242,1618,3460,4807,1544,5793,1793,3402,1533,4623,6031,5348,6017,5967,6764,3745,5589,4097,2918,3044,2448,4638,15254,1063,1354,930,1458,5120,3530,3794,4633,3439,1756,5906,2035,3332,5755,4110,4220,4528,2184,5674,1988,3414,6551,5005,2580,945,3313,3103,1835,5740,5252,5977,5935,5921,4803,3466,1475,5874,2405,1228,4775,5352,2957,2763,5486,1782,4079,4266,3730,5825,5938,5770,3898,2082,2400,6483,5750,1703,1709,3195,7696,2755,3061,3485,1826,5160,5182,9230,949,4637,12351,1409,5953,3976,2603,4524,4956,1660,2339,3046,4415,5759,4654,1264,1323,3148,3653,1313,4275,1832,934,6006,5989,1132,3855,5744,3517,1572,5480,5829,5746,4460,3180,4771,5617,1232,1922,6010,1892,5868,5256,4353,5866,5521,6905,30643,2552,12319,5802,1115,2929,5727,3835,3708,2989,1362,4507,4400,2456,5888,4600,2451,3473,1136,3525,4724,1020,1051,5834,5787,2222,4696,2237,1415,5264,924,6002,3322,5892,2794,4583,1714,4443,3075,1450,2090,3393,2996,3724,1040,2893,1632,3670,2259,4001,40742,5333,3163,1828,2925,5804,5156,937,3569,30853,5985,4871,1960,3300,5761,4686,5360,3152,981,5220,988,2750,3870,2392,8742,3986,5929,2367,3537,3068,4230,5401,3189,58083,5384,5101,956,5772,1796,1394,5296,998,3955,2809,1943,1201,6327,2965,5665,4519,3588,1242,3559,5819,3492,3406,3184,2982,4700,2922,5961,3229,920,3450,5751,5017,3186,2118,1338,2047,1470,4925,3679,4216,5783,3591,2910,2204,3303,4962,6015,2574,3169,30852,4480,925,5545,5070,5416,2737,3767,2296,2621,2790,5281,1636,2441,4466,2596,1255,1123,4204,4499,3778,3261,12385,4712,2601,3827,3711,2560,3972,3603,6000,1042,952,8994,1570,1174,4252,5956,4521,30577,1824,5754,2032,30847,3814,2396,3682,3471,1560,3948,5983,9190,2433,7503,4402,4979,2213,2345,1195,3727,58042,916,3166,3980,1837,3090,12321,3198,2332,2826,2820,4994,3297,8736,4385,1951,5534,3600,5988,3894,5779,9613,1634,1392,3647,2112,5330,5515,3595,3445,1012,5066,1402,1143,3254,948,8282,4048,4525,4233,5362,2631,4219,5854,1936,4123,1360,5189,3105,5626,3909,5904,1259,3122,2946,5238,5673,1121,4486,5798,1227,980,4636,8063,1138,4930,4227,5951,989,3087,4898,30855,4676,2798,5830,5166,3143,8105,933,5743,8346,1644,3294,3573,3141,3311,25710,2323,2830,5107,30860,3094,1461,3441,3010,5464,5786,2080,5253,1414,2196,4744,2613,5932,6763,2172,4648,3428,5662,2349,1612,2978,2781,4530,3242,3703,1249,3541,5374,1266,3743,1974,984,2566,4231,4135,3333,5369,3005,2140,3654,985,1456,1382,1552,2851,5973,9201,3222,2497,6005,5305,2766,3692,2482,2272,3364,3083,3201,1627,4361,1333,3755,5747,3802,938,4081,4889,5833,1712,6070,5737,1071,5513,926,5170,3454,8739,2761,6486,35515,4765,2883,921,2076,1170,3639,4448,6688,5930,8609,5249,5840,953,5872,3675,4995,1732,2121,2729,1727,2176,2292,5762,3257,4874,8040,30837,9181,5979,4489,2894,3343,9677,4116,1103,4340,3888,7165,2524,2376,21695,5241,1916,2789,5844,1752,4801,5831,5612,3458,2398,6019,4946,5022,3213,5720,3372,4662,5456,5933,3070,2970,3319,3636,3234,2938,4283,1784,5488,2188,12317,5940,3945,5050,1535,5876,4381,5271,4590,1520,5752,5039,5908,5859,4822,4060,1765,4273,947,4526,5185,3773,936,5033,3751,2220,1707,5118,5363,3051,5471,2891,3726,2308,4149,3663,4218,5086,8492,3487,2055,919,4640,979,4704,5212,5671,2642,2084,3038,1574,3515,5880,4300,3586,1376,5870,4790,2415,5103,5827,3270,2257,990,1933,4616,3197,1801,3160,1307,5202,5082,4264,2757,4332,52436,4296,3583,2289,5410,1061,21731,3456,18558,2824,4694,4635,2182,6004,2812,1080,4882,3055,1557,2343,3668,4462,4911,5994,3073,4064,4818,3572,1909,4452,9674,4993,4990,5987,2578,983,4720,4232,959,1213,9294,2086,3917,1000,4196,6029,8457,5742,2962,5254,5775,5931,2725,1594,2051,3423,12556,3806,2369,1015,4827,986,2633,5849,1477,3706,4954,2967,2390,3512,3178,5693,3348,5089,3876,922,4965,2867,21689,3490,3380,1562,5424,3193,5886,5785,2878,3292,4741,5688,5959,5881,944,4813,2994,927,5757,2124,6191,5952,6962,5678,4566,4859,2202,939,6076,5916,1018,2564,3278,4581,15252,5763,5358,5133,5991,3571,1798,5716,4035,971,2143,5748,3833,3129,1368,4894,4377,4324,2888,5790,993,58120,5452,1748,7166,2863,5927,5602,5514,57758,5250,3112,4937,5388,1225,4366,1605,2588,4950,1780,3209,3246,4346,4398,1716,2920,1186,5015,1038,5753,4222,7667,3127,1658,2599,4737,5638,5450,4875,2656,3019,5684,3448,4522,5731,4190,3818,1452,3114,5912,6093,1262,1235,2276,2128,8206,8644,3623,3697,3652,5675,3124,4611,4488,9622,1008,8433,5596,12665,3398,1404,2247,5147,2558,6073,4246,5998,3356,5240,1955,2843,2145,15240,4106,5809,4046,58248,1140,4634,2807,3156,3914,3684,6622,1240,4217,991,3400,2458,1918,6013,4997,4185,6938,3625,3056,5184,3593,2865,5832,2875,5771,4639,3284,3139,5981,2479,6965,4606,5179,2045,1180,5653,931,2885,4873,2078,2743,2997,3346,2110,1390,5124,1646,2855,4089,2532,4250,12516,5426,3748,6910,3561,4527,12527,5055,961,2594,5724,2283,1903,4666,4683,3383,3369,4042,22025,1629,3104,6003,6023,5813,4495,3859,3331,3136,3252,5505,4969,1558,2152,3978,3694,3324,5164,4214,3677,1607,5739,2902,1309,5704,4025,2421,1030,5963,6045,3598,5837,929,3896,2198,5128,2315,2494,4570,4372,2623,3761,9839,5864,1348,2287,4794,1725,4809,5268,5430,3464,8574,4357,5247,5760,3203,5677,6055,1578,4472,4399,2385,3785,5971,6007,3997,5796,3264,5537,5078,4523,4841,1986,4579,9944,3015,918,5300,1816,8207,2186,4631,2746,3716,2704,1288,4193,3843,5440,2783,5559,3145,5741,2417,2714,3426,5251,3030,58061,960,1473,3673,5283,2063,1610,4318,1742,2353,1352,1129,46924,4066,992,8730,4831,5046,5354,6911,15287,2270,4221,2241,987,4848,8328,3701,4242,9679,4876,5975,1550,5768,4229,982,1004,3812,8570,5344,3341,3474,3528,5591,30854,935,2998,2832,1416,3432,3296,3013,3960,3437,5029,2321,940,3924,5986,923,5789,4784,2887,2074,5788,2436,1848,2059,2438,5255,3443,5445,2615,1769,2453,4056,15272,2834,5732,6035,3200,2106,3553,7424,3047,4940,3575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP034+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n018.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 20:41:39 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.80/2.73 % [INFO] Parsing done (1722ms).
% 6.80/2.76 % [INFO] Running in sequential loop mode.
% 7.25/3.12 % [INFO] eprover registered as external prover.
% 7.25/3.13 % [INFO] Scanning for conjecture ...
% 10.65/4.04 % [INFO] Found a conjecture (or negated_conjecture) and 13512 axioms. Running axiom selection ...
% 14.07/6.33 % [INFO] Axiom selection finished. Selected 913 axioms (removed 12599 axioms).
% 16.02/7.04 % [INFO] Problem is first-order (TPTP FOF).
% 16.02/7.11 % [INFO] Type checking passed.
% 16.02/7.12 % [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 ...
% 258.18/96.15 % External prover 'e' found a proof!
% 258.18/96.15 % [INFO] Killing All external provers ...
% 258.18/96.15 % Time passed: 95588ms (effective reasoning time: 93389ms)
% 258.18/96.15 % 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)>
% 258.18/96.16 % Axioms used in derivation (913): t4_tsep_1, t29_tsep_1, t72_xboole_1, cc31_tex_2, cc17_tex_3, d4_tex_4, fc3_tex_2, t48_tex_3, fc1_t_0topsp, d4_tex_3, rc6_tdlat_3, d1_tsp_1, t9_tex_3, fc8_tops_1, t12_tex_2, d5_tdlat_3, t76_tex_4, cc4_tsp_2, t11_tsp_1, cc1_tops_1, t32_tsep_1, cc24_tex_2, t15_lopclset, t52_tex_2, t20_tex_2, t14_tsp_1, t8_tex_4, t51_tex_2, t60_tex_2, t27_pcomps_1, t16_compts_1, d6_tex_2, cc44_tex_2, t18_tex_2, t19_xboole_1, t80_tex_4, cc10_tsp_2, t17_xboole_1, t2_lopclset, t18_tsep_1, t42_subset_1, t43_subset_1, rc18_tex_2, t6_tex_4, t35_subset_1, rc7_tdlat_3, t26_tops_3, t16_tsep_1, t53_tex_2, t54_tops_1, d6_t_0topsp, rc11_tdlat_3, rc3_tdlat_3, t45_pre_topc, t38_tex_3, cc2_tex_2, t53_subset_1, t8_pcomps_1, t35_tops_1, d1_tex_3, t41_pre_topc, idempotence_k3_xboole_0, t9_tsp_2, t45_tdlat_3, t23_xboole_1, cc40_tex_2, t91_tex_4, d14_tex_4, redefinition_k5_subset_1, redefinition_m2_tsp_1, d12_borsuk_1, t73_xboole_1, dt_k5_tex_4, t25_tsep_1, t79_tops_1, t12_tops_3, t62_tops_3, cc8_tsp_1, t105_zfmisc_1, dt_k19_borsuk_1, t65_tex_3, cc5_tsp_2, t15_tsep_1, cc3_tex_4, cc14_tex_3, t7_subset_1, t91_tops_1, t23_tex_2, t33_tops_2, cc2_tsp_1, t28_tex_3, cc6_tdlat_3, t46_tex_4, t4_topmetr, t35_tsep_1, t53_tdlat_3, d2_tops_3, t45_tex_4, t13_tex_2, dt_k20_borsuk_1, t113_xboole_1, rc4_pre_topc, rc20_tex_2, t25_tops_3, t35_borsuk_1, t1_subset, t43_tex_3, existence_l1_funcsdom, t19_tex_3, rc12_tex_2, t8_subset_1, t81_tops_3, t16_tsp_1, d1_pcomps_1, rc3_tops_1, fc6_tex_4, t79_tops_3, t4_ordinal1, t4_tex_3, t28_tex_2, t12_tex_3, dt_k2_tsep_1, cc6_tsp_2, t8_tex_3, t71_tex_4, t21_tex_2, d7_tex_2, fc4_tops_1, t18_xboole_1, cc37_tex_2, t11_t_0topsp, t74_tex_4, t6_xboole_1, redefinition_k4_tsp_2, t70_xboole_1, t74_tsep_1, dt_k7_tex_4, t6_tsep_1, cc8_tex_4, fc4_subset_1, dt_k1_tops_1, l19_tsp_2, t81_zfmisc_1, t22_compts_1, t97_tsep_1, t7_tex_4, t9_tsep_1, t5_t_0topsp, t68_xboole_1, d16_tex_4, t25_xboole_1, cc7_tdlat_3, rc7_tex_3, cc23_tex_3, fc11_tops_1, cc20_tex_3, d6_pre_topc, d11_borsuk_1, t45_tops_3, t55_tops_3, t23_tops_3, cc43_tex_2, cc1_tex_3, d10_borsuk_1, t24_tex_2, t24_tdlat_3, 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, redefinition_k1_pcomps_1, dt_k16_borsuk_1, t34_tex_3, t23_tsep_1, dt_m2_tsp_1, t82_tops_1, dt_m1_borsuk_1, cc5_tops_1, t73_tex_3, t15_tops_3, t47_tops_3, t61_tex_2, rc1_tdlat_3, t3_tdlat_3, t49_tex_2, t56_tops_1, t23_tdlat_3, symmetry_r4_tsep_1, cc1_tsp_1, t27_tex_3, t49_tex_3, t99_tsep_1, d1_tsep_1, d3_tex_4, t29_tex_2, t32_tops_2, t3_lopclset, t68_borsuk_1, cc33_tex_2, t32_tops_1, cc18_tex_3, t78_borsuk_1, t8_tsp_1, fc21_tex_4, t9_xboole_1, cc3_tops_1, cc3_tsp_2, t36_subset_1, t70_tsep_1, t4_tsp_2, cc16_tex_2, t66_tex_3, rc3_pre_topc, t3_topmetr, rc4_tdlat_3, idempotence_k5_subset_1, symmetry_r3_tsep_1, t13_tsp_2, t21_tsp_1, t38_tops_3, t81_tsep_1, t11_tsp_2, commutativity_k3_xboole_0, t27_tops_3, t115_zfmisc_1, t35_tex_2, t48_tops_3, t50_tops_1, t137_zfmisc_1, t51_tex_3, rc4_tex_3, t32_subset_1, rc4_tsp_1, rc6_pre_topc, t31_tops_3, t12_t_0topsp, t26_tdlat_3, t5_tex_2, rc3_tsp_1, t34_tops_1, t75_tex_2, t20_tsp_1, fc5_pre_topc, involutiveness_k3_subset_1, fc2_xboole_0, t16_lopclset, t60_tops_3, d14_tsp_1, existence_l2_quantal1, t34_tsep_1, cc29_tex_2, cc25_tex_2, t53_tex_3, t85_tex_4, cc11_tex_3, t108_xboole_1, t43_tops_1, t52_pre_topc, rc1_tops_1, d14_borsuk_1, t33_tdlat_3, t27_tex_2, cc2_tex_4, t73_tops_3, t60_tex_3, rc5_tex_3, t72_tex_3, t19_tsep_1, t48_tex_2, t16_tex_4, dt_m1_eqrel_1, dt_k21_borsuk_1, t37_tops_3, t20_tex_3, t22_tsep_1, t17_tex_2, t40_tex_3, rc17_tex_2, cc1_tex_2, t14_lopclset, t78_tops_3, dt_k11_borsuk_1, t12_tsp_2, fc2_borsuk_1, t46_tex_3, t53_tops_3, t18_tex_3, t9_tops_3, dt_k1_lopclset, t74_borsuk_1, redefinition_k19_borsuk_1, cc2_tsp_2, t10_compts_1, t118_zfmisc_1, t91_tsep_1, t77_borsuk_1, t61_tops_3, t92_tsep_1, t13_t_0topsp, rc2_subset_1, t19_tex_2, dt_k6_subset_1, t43_pre_topc, t35_tops_3, t13_tsep_1, t1_xboole_1, free_g1_pre_topc, cc8_tex_3, t41_tops_1, cc9_tdlat_3, t65_tex_2, commutativity_k2_xboole_0, t5_subset, rc1_tex_4, t9_compts_1, t4_tsp_1, cc19_tex_2, rc5_tsp_1, t73_tex_4, t30_tsep_1, t10_tops_3, cc9_tex_3, rc3_funcsdom, t42_tdlat_3, t67_tex_2, commutativity_k1_tsep_1, t22_tops_1, cc15_tex_3, t75_xboole_1, cc11_tdlat_3, t76_tsep_1, t20_tops_3, t2_tex_3, cc6_tex_4, t36_tsep_1, cc4_tex_3, t84_borsuk_1, t123_zfmisc_1, t40_tex_2, t46_tops_1, t4_xboole_0, t62_tex_2, d12_tsp_1, t17_tsp_1, t95_tsep_1, d8_tsp_1, t27_tops_1, fc19_tex_4, commutativity_k5_subset_1, t79_borsuk_1, d5_tops_1, t44_tdlat_3, fc2_tops_1, t44_tex_3, t41_tops_3, dt_k1_tex_2, t42_tex_3, cc15_tdlat_3, cc47_tex_2, cc30_tex_3, t79_zfmisc_1, rc7_tsp_1, t63_tex_3, t86_tex_4, t15_tsp_1, t34_tops_2, t68_tops_3, t7_tdlat_3, t3_tex_3, t10_tex_3, t2_tarski, d1_tex_4, t24_tex_3, d4_tsp_1, t7_tex_3, rc9_tdlat_3, rc19_tex_2, dt_k18_borsuk_1, cc22_tex_3, t16_tops_3, cc15_tex_2, t79_tex_4, t19_tops_3, t83_tops_3, t89_tex_4, cc7_tsp_1, t57_tops_1, cc18_tex_2, t84_tops_3, t71_tex_3, t43_tdlat_3, t75_borsuk_1, rc4_quantal1, t114_xboole_1, d11_tsp_1, t52_subset_1, t5_ordinal1, redefinition_v3_tsp_1, fc3_xboole_0, d2_xboole_0, t1_tsp_2, cc12_tdlat_3, cc31_tex_3, cc49_tex_2, dt_k22_borsuk_1, abstractness_v1_pre_topc, rc11_tex_3, t98_tsep_1, d9_tsp_1, t32_tops_3, t30_tex_3, t10_t_0topsp, t73_tsep_1, t52_tex_3, t21_xboole_1, t45_tex_2, d5_pre_topc, t4_subset, cc11_tsp_1, cc38_tex_2, t76_xboole_1, t53_pre_topc, t81_tops_1, t30_tdlat_3, t30_xboole_1, cc6_tsp_1, t39_tops_1, t96_tsep_1, t78_tsep_1, fc2_pcomps_1, t33_tsep_1, t36_tex_2, rc16_tex_2, t44_tops_3, t52_tops_1, t72_borsuk_1, d12_tex_4, t83_tsep_1, fraenkel_a_3_1_pcomps_1, t47_tex_3, t30_tops_1, t14_connsp_2, t15_tex_2, t41_borsuk_1, t58_tops_1, rc15_tex_2, t29_xboole_1, t46_tdlat_3, d5_tex_2, rc2_tex_4, t72_tsep_1, t7_tsep_1, t139_zfmisc_1, t18_tex_4, t74_tops_3, t7_boole, fraenkel_a_2_3_borsuk_1, t25_tex_2, t14_tsep_1, fc9_tops_1, t58_tex_2, t31_tops_2, dt_g1_pre_topc, cc28_tex_3, dt_k6_borsuk_1, t7_tsp_1, cc13_tex_3, rc6_tsp_1, redefinition_k2_tsp_2, t25_tdlat_3, cc35_tex_2, t18_compts_1, d2_subset_1, t55_tex_2, t3_t_0topsp, fc1_subset_1, d4_tops_3, cc4_tex_4, t58_tops_3, t5_tex_3, rc3_tex_2, rc1_t_0topsp, t3_ordinal1, t82_tops_3, t75_tex_3, d5_t_0topsp, cc21_tex_3, rc14_tex_2, t3_tsp_2, t16_subset_1, rc10_tex_3, t92_tops_1, t7_ordinal1, d8_tex_2, rc1_subset_1, t72_tex_4, t61_tex_3, t16_tex_3, t39_tdlat_3, rc8_tdlat_3, t90_tsep_1, t15_tex_3, t11_tops_3, rc11_tex_2, cc26_tex_2, t22_tex_3, dt_m1_pre_topc, t31_xboole_1, cc14_tex_2, cc16_tex_3, t24_xboole_1, t80_tsep_1, t46_tex_2, t90_tex_4, t68_tex_3, t20_compts_1, t69_xboole_1, rc10_tdlat_3, t87_tsep_1, t67_tops_3, d3_tsp_2, t20_xboole_1, t47_pre_topc, t3_tops_3, t124_zfmisc_1, t62_tex_3, cc2_tex_3, dt_k6_tex_4, fc1_tex_4, cc29_tex_3, t2_tsp_2, cc22_tex_2, t70_borsuk_1, t86_tsep_1, fc5_borsuk_1, rc8_tex_3, t56_tex_2, rc13_tex_3, t37_tex_3, cc19_tex_3, t8_tsep_1, existence_m2_tsp_1, t78_tex_4, t55_tops_1, t57_tex_3, t85_tsep_1, d5_tsep_1, t93_tops_1, existence_m1_pre_topc, dt_k3_t_0topsp, t21_tsep_1, t77_tops_3, t40_tops_3, t94_tsep_1, cc1_eqrel_1, t59_tex_3, cc27_tex_3, redefinition_k21_borsuk_1, t17_tex_3, cc7_tex_3, t52_tdlat_3, t85_borsuk_1, t120_zfmisc_1, t4_tdlat_3, t31_subset_1, t3_subset, cc10_tex_3, redefinition_k3_tsp_2, t52_borsuk_1, t64_tex_2, t39_tops_3, cc5_tex_3, existence_m1_subset_1, d1_tdlat_3, cc4_tsp_1, t42_borsuk_1, t32_tex_3, t42_tex_2, t35_tex_3, t13_tex_3, rc1_tex_3, t54_tops_3, dt_k2_t_0topsp, t38_tops_1, t81_tex_4, t14_tex_3, cc14_tdlat_3, rc4_tex_2, t14_xboole_1, t44_setfam_1, d2_tex_4, t41_tdlat_3, t18_tsp_1, t75_tsep_1, existence_m1_tsp_1, t10_tsp_2, t56_tex_3, t54_pre_topc, cc6_tex_3, t88_tex_4, rc2_tsep_1, t23_tex_3, t70_tex_3, t21_compts_1, t48_tops_1, symmetry_r1_tsep_1, d1_zfmisc_1, t16_xboole_1, t4_t_0topsp, cc2_tops_1, t51_pre_topc, t29_tdlat_3, t26_xboole_1, t63_xboole_1, t11_tex_3, d3_tex_3, t74_tex_3, rc2_tex_3, t82_tsep_1, cc4_tdlat_3, dt_k5_subset_1, rc3_pcomps_1, cc36_tex_2, cc32_tex_2, cc3_tdlat_3, t12_tsep_1, d7_tsp_2, t5_tsep_1, t51_subset_1, t26_tex_2, t2_tsep_1, cc9_tsp_1, t8_tdlat_3, rc1_tsp_2, cc41_tex_2, t45_tops_1, t24_tsep_1, d9_pre_topc, t25_tex_3, t18_tdlat_3, cc7_tsp_2, t26_pcomps_1, t26_subset_1, t51_tops_1, rc2_tsp_1, t22_xboole_1, t47_tex_4, t76_tops_3, cc12_tex_2, t17_tdlat_3, t40_tdlat_3, cc26_tex_3, d3_tarski, t28_pcomps_1, t77_tsep_1, fc1_lopclset, d4_tsp_2, t13_xboole_1, t50_tex_3, d3_tsep_1, t83_zfmisc_1, t17_subset_1, t69_tex_4, reflexivity_r1_tarski, t41_tex_2, t8_xboole_1, t71_tsep_1, cc46_tex_2, t78_xboole_1, t28_xboole_1, cc2_tdlat_3, t82_borsuk_1, d7_tex_4, t46_subset_1, t19_tex_4, t88_tsep_1, d2_tsep_1, fc2_tex_2, existence_l1_pre_topc, t5_xboole_0, t119_zfmisc_1, t47_tex_2, t121_zfmisc_1, t17_tex_4, t83_tex_4, cc3_tex_3, d8_tsp_2, fraenkel_a_1_0_lopclset, t54_tex_3, t2_topmetr, t75_tops_3, t55_tex_3, t41_tex_3, fc1_pcomps_1, rc2_tdlat_3, d10_tsp_1, redefinition_m1_tsp_1, t72_tops_3, t17_tsep_1, rc3_tex_3, t32_tdlat_3, cc7_tex_4, t9_tex_4, t4_xboole_1, t11_compts_1, fc15_tex_4, cc21_tex_2, t17_compts_1, t1_partfun1, rc1_pre_topc, t93_tsep_1, rc5_tdlat_3, rc7_pre_topc, d2_tsp_1, cc28_tex_2, cc23_tex_2, rc13_tex_2, d4_tex_2, t69_tex_3, t40_tsep_1, t45_tex_3, t53_tops_1, d5_tops_3, t56_tops_3, cc17_tex_2, d4_compts_1, t49_pre_topc, t47_subset_1, t2_tsp_1, t31_tops_1, d18_tex_4, t84_tex_4, cc13_tex_2, rc3_borsuk_1, t85_tops_3, t68_tsep_1, existence_m1_eqrel_1, redefinition_v2_tsp_1, cc10_tdlat_3, dt_k2_pcomps_1, cc12_tex_3, t20_tsep_1, t127_zfmisc_1, t44_subset_1, rc2_tops_1, t10_pcomps_1, cc5_tex_4, t77_xboole_1, t11_xboole_1, cc50_tex_2, fc3_tops_1, dt_u1_pre_topc, cc30_tex_2, rc9_tex_3, t54_subset_1, t59_tex_2, t39_pre_topc, t4_lopclset, d1_lopclset, t64_xboole_1, fc4_borsuk_1, t68_tex_4, t69_tops_3, cc13_tdlat_3, t8_boole, cc13_tsp_1, rc1_xboole_0, t47_tops_1, t59_tops_3, d3_tsp_1, t58_tex_3, rc2_tex_2, t48_pre_topc, t2_subset, t64_tex_3, rc2_pcomps_1, t31_tsep_1, cc48_tex_2, cc10_tsp_1, existence_m1_borsuk_1, t64_tops_3, fc5_tex_4, rc1_tsp_1, cc4_tops_1, t6_tex_3, cc20_tex_2, t12_xboole_1, rc4_borsuk_1, t7_pcomps_1, t10_tsep_1, d5_tsp_1, t1_tex_3, d5_borsuk_1, t47_tdlat_3, symmetry_r1_xboole_0, cc39_tex_2, t39_tex_3, t37_tex_2, d3_tops_1, t70_tops_3, dt_k1_pcomps_1, rc1_pcomps_1, d4_tops_1, fc14_tex_4, cc8_tdlat_3, dt_k1_tsep_1, t74_xboole_1, fc3_tex_4, t65_tops_3, t67_tex_3, t13_tsp_1, t66_tops_3, idempotence_k2_xboole_0, t48_subset_1, cc1_tdlat_3, t73_tex_2, cc42_tex_2, t57_tops_3, t89_tsep_1, cc24_tex_3, t40_tops_1, cc8_tsp_2, rc2_pre_topc, cc45_tex_2, d10_xboole_0, t21_tex_3, fc18_tex_4, cc5_tsp_1, t71_borsuk_1, t44_tex_4, t7_xboole_1, cc1_tex_4, d15_borsuk_1, redefinition_k20_borsuk_1, t33_tops_3, t5_xboole_1, t79_tex_2, t70_tex_4, t3_xboole_0, t13_lopclset, t6_ordinal1, t1_tsep_1, d13_tsp_1, fc4_tex_2, t25_pcomps_1, d1_tops_1, cc34_tex_2, t5_tsp_1, t29_tex_3, t80_tops_3, t49_subset_1, rc1_tsep_1, t7_tarski, t57_tex_2, t75_tex_4, t34_tex_2, t19_tsp_1, cc5_tdlat_3, t33_tex_3, t36_tops_3, d7_t_0topsp, t31_tex_3, t6_tsp_1, rc5_pre_topc, t16_tex_2, t79_tsep_1, cc3_tsp_1, t11_tsep_1, cc32_tex_3, rc2_xboole_0, t44_tops_1, dt_k6_pre_topc, t63_tops_3, d13_tex_4, cc9_tsp_2, cc25_tex_3, t22_tops_3, t2_tdlat_3, t43_tex_2, dt_m1_tsp_1, t14_tex_2, t26_tops_1, cc12_tsp_1, d6_tsp_1, t54_tdlat_3, fc16_tex_4, d3_tex_2, t24_tops_3, t10_xboole_1, dt_k3_subset_1, t26_tex_3, t46_tops_3, t73_borsuk_1, t18_tops_3, cc1_tsp_2, antisymmetry_r2_hidden, d7_tsp_1, t82_tex_4, t29_tops_3, t29_tops_1, d3_xboole_0, t66_tex_2, t11_pcomps_1, t42_pre_topc, cc27_tex_2, d4_tdlat_3, cc1_pre_topc, d2_tex_3
% 258.18/96.16 % No. of inferences in proof: 2385
% 258.18/96.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 95588 ms resp. 93389 ms w/o parsing
% 262.84/97.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 262.84/97.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------