TSTP Solution File: TOP047+1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : TOP047+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:17:35 EDT 2024
% Result : Theorem 83.15s 14.16s
% Output : Refutation 83.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 143
% Syntax : Number of formulae : 236 ( 25 unt; 52 typ; 0 def)
% Number of atoms : 722 ( 49 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 1890 ( 97 ~; 2 |; 333 &;1255 @)
% ( 6 <=>; 197 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 2 con; 0-3 aty)
% Number of variables : 330 ( 0 ^ 267 !; 63 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_orders_2_type,type,
v2_orders_2: $i > $o ).
thf(v3_orders_2_type,type,
v3_orders_2: $i > $o ).
thf(v4_orders_2_type,type,
v4_orders_2: $i > $o ).
thf(v24_waybel_0_type,type,
v24_waybel_0: $i > $o ).
thf(v25_waybel_0_type,type,
v25_waybel_0: $i > $o ).
thf(v2_lattice3_type,type,
v2_lattice3: $i > $o ).
thf(l1_orders_2_type,type,
l1_orders_2: $i > $o ).
thf(g1_orders_2_type,type,
g1_orders_2: $i > $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(u1_orders_2_type,type,
u1_orders_2: $i > $i ).
thf(k14_yellow_6_type,type,
k14_yellow_6: $i > $i > $i ).
thf(k3_waybel28_type,type,
k3_waybel28: $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v3_relat_1_type,type,
v3_relat_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(m4_yellow_6_type,type,
m4_yellow_6: $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(l1_pre_topc_type,type,
l1_pre_topc: $i > $o ).
thf(l1_waybel_0_type,type,
l1_waybel_0: $i > $i > $o ).
thf(g1_pre_topc_type,type,
g1_pre_topc: $i > $i > $i ).
thf(v1_pre_topc_type,type,
v1_pre_topc: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(v2_tops_1_type,type,
v2_tops_1: $i > $i > $o ).
thf(v2_pre_topc_type,type,
v2_pre_topc: $i > $o ).
thf(v3_pre_topc_type,type,
v3_pre_topc: $i > $i > $o ).
thf(v4_pre_topc_type,type,
v4_pre_topc: $i > $i > $o ).
thf(u1_pre_topc_type,type,
u1_pre_topc: $i > $i ).
thf(a_2_1_yellow_6_type,type,
a_2_1_yellow_6: $i > $i > $i ).
thf(v3_tops_1_type,type,
v3_tops_1: $i > $i > $o ).
thf(v1_yellow_0_type,type,
v1_yellow_0: $i > $o ).
thf(v1_orders_2_type,type,
v1_orders_2: $i > $o ).
thf(v7_waybel_0_type,type,
v7_waybel_0: $i > $o ).
thf(r1_waybel_0_type,type,
r1_waybel_0: $i > $i > $i > $o ).
thf(12,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(142,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m4_yellow_6 @ B @ A ) )
=> ( ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
& ( l1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_yellow_6) ).
thf(411,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m4_yellow_6 @ B @ A ) )
=> ( ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
& ( l1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(8,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(129,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(259,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(92,axiom,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v7_waybel_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_6) ).
thf(445,plain,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v7_waybel_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(16,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(154,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(71,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_waybel_0 @ B @ A )
=> ( l1_orders_2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(347,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_waybel_0 @ B @ A )
=> ( l1_orders_2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(78,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(365,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(11,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(138,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(69,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(333,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(249,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(83,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(408,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(4,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(115,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
& ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(276,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
& ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(44,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(247,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(91,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(440,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(52,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(269,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(417,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(60,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(301,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(184,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(70,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v2_tops_1 @ B @ A ) )
=> ( ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(344,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v2_tops_1 @ B @ A ) )
=> ( ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
= ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
=> ( ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) )
= ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel33) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
= ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
=> ( ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) )
= ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(93,plain,
~ ! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
= ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
=> ( ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) )
= ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(284,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(15,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m4_yellow_6 @ B @ A )
=> ( v1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_yellow_6) ).
thf(152,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m4_yellow_6 @ B @ A )
=> ( v1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(58,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(289,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(164,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(179,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(59,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(292,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(39,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(233,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(220,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(72,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(349,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(88,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( m4_yellow_6 @ ( k3_waybel28 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_waybel28) ).
thf(424,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( m4_yellow_6 @ ( k3_waybel28 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(26,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(192,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(252,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(81,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_pre_topc @ A )
=> ( A
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(403,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_pre_topc @ A )
=> ( A
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(188,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(67,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
= ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
=> ( r1_tarski @ ( u1_pre_topc @ ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) ) ) @ ( u1_pre_topc @ ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_waybel33) ).
thf(328,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
= ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
=> ( r1_tarski @ ( u1_pre_topc @ ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) ) ) @ ( u1_pre_topc @ ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(256,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(237,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(51,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(266,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(76,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_orders_2 @ A )
=> ( A
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(360,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_orders_2 @ A )
=> ( A
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(64,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(311,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(279,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(149,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(82,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(406,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(38,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(230,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(245,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(61,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(303,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i,D: $i] :
( ( ( g1_pre_topc @ A @ B )
= ( g1_pre_topc @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(271,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i,D: $i] :
( ( ( g1_pre_topc @ A @ B )
= ( g1_pre_topc @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(32,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(213,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(29,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(198,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m4_yellow_6 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
& ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc24_yellow_6) ).
thf(306,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m4_yellow_6 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
& ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(10,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(135,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(226,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(90,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(438,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(89,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(426,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(162,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( m4_yellow_6 @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_1_yellow_6 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ E @ D )
=> ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v3_orders_2 @ F )
& ( v7_waybel_0 @ F )
& ( l1_waybel_0 @ F @ B ) )
=> ( ( r2_hidden @ ( k4_tarski @ F @ E ) @ C )
=> ( r1_waybel_0 @ B @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow_6) ).
thf(374,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( m4_yellow_6 @ C @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_yellow_6 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ E @ D )
=> ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v3_orders_2 @ F )
& ( v7_waybel_0 @ F )
& ( l1_waybel_0 @ F @ B ) )
=> ( ( r2_hidden @ ( k4_tarski @ F @ E ) @ C )
=> ( r1_waybel_0 @ B @ F @ D ) ) ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ E @ D )
=> ! [F: $i] :
( ( ~ ( v3_struct_0 @ F )
& ( v3_orders_2 @ F )
& ( v7_waybel_0 @ F )
& ( l1_waybel_0 @ F @ B ) )
=> ( ( r2_hidden @ ( k4_tarski @ F @ E ) @ C )
=> ( r1_waybel_0 @ B @ F @ D ) ) ) ) ) )
=> ( r2_hidden @ A @ ( a_2_1_yellow_6 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(3,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(112,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(123,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(194,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(56,axiom,
? [A: $i] : ( l1_pre_topc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(282,plain,
? [A: $i] : ( l1_pre_topc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
& ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
& ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(182,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(68,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(331,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m4_yellow_6 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
& ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
& ( v2_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc25_yellow_6) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m4_yellow_6 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
& ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
& ( v2_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(77,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v3_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(363,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v3_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(203,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(66,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m4_yellow_6 @ B @ A )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( k14_yellow_6 @ A @ B ) )
<=> ( ( ( u1_struct_0 @ C )
= ( u1_struct_0 @ A ) )
& ( ( u1_pre_topc @ C )
= ( a_2_1_yellow_6 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d27_yellow_6) ).
thf(319,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m4_yellow_6 @ B @ A )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( C
= ( k14_yellow_6 @ A @ B ) )
=> ( ( ( u1_struct_0 @ C )
= ( u1_struct_0 @ A ) )
& ( ( u1_pre_topc @ C )
= ( a_2_1_yellow_6 @ A @ B ) ) ) )
& ( ( ( ( u1_struct_0 @ C )
= ( u1_struct_0 @ A ) )
& ( ( u1_pre_topc @ C )
= ( a_2_1_yellow_6 @ A @ B ) ) )
=> ( C
= ( k14_yellow_6 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(73,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(351,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(119,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] : ( m4_yellow_6 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m4_yellow_6) ).
thf(235,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] : ( m4_yellow_6 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(65,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(315,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(13,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(146,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(87,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(422,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(50,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(262,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(42,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(242,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(75,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(358,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(9,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(131,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(200,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(47,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ? [B: $i] : ( l1_waybel_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(254,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ? [B: $i] : ( l1_waybel_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(74,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v1_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(354,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v1_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(63,axiom,
? [A: $i] : ( l1_orders_2 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(309,plain,
? [A: $i] : ( l1_orders_2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(215,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26420,plain,
$false,
inference(e,[status(thm)],[142,411,129,259,445,154,347,365,138,333,249,408,115,276,247,440,269,417,301,184,344,196,157,93,284,152,289,164,179,292,233,220,349,424,192,252,224,403,188,328,256,237,266,360,311,279,149,406,230,245,303,271,213,198,306,135,226,438,426,162,374,112,123,194,282,414,182,331,370,363,203,319,351,186,119,235,315,146,422,168,262,242,126,358,131,200,254,354,309,215,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : TOP047+1 : TPTP v8.2.0. Released v3.4.0.
% 0.04/0.09 % Command : run_Leo-III %s %d
% 0.08/0.29 % Computer : n012.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Sat May 18 11:27:54 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.78/0.73 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.90 % [INFO] Parsing done (161ms).
% 1.21/0.90 % [INFO] Running in sequential loop mode.
% 1.63/1.14 % [INFO] eprover registered as external prover.
% 1.63/1.14 % [INFO] cvc4 registered as external prover.
% 1.63/1.15 % [INFO] Scanning for conjecture ...
% 1.98/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 101 axioms. Running axiom selection ...
% 2.18/1.34 % [INFO] Axiom selection finished. Selected 90 axioms (removed 11 axioms).
% 2.56/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.62/1.49 % [INFO] Type checking passed.
% 2.62/1.49 % [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 ...
% 83.15/14.15 % External prover 'e' found a proof!
% 83.15/14.15 % [INFO] Killing All external provers ...
% 83.15/14.15 % Time passed: 13761ms (effective reasoning time: 13246ms)
% 83.15/14.15 % 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)>
% 83.15/14.16 % Axioms used in derivation (90): fc4_subset_1, rc1_tops_1, cc6_tops_1, abstractness_v1_orders_2, dt_l1_orders_2, fc25_yellow_6, rc3_finset_1, existence_l1_struct_0, fc14_finset_1, antisymmetry_r2_hidden, redefinition_m2_relset_1, cc1_tops_1, cc2_finset_1, dt_k14_yellow_6, rc4_finset_1, l12_waybel33, d5_tarski, t1_subset, rc3_tops_1, fc4_relat_1, d27_yellow_6, cc5_tops_1, rc3_funct_1, rc4_yellow_6, cc3_tops_1, dt_m2_relset_1, cc1_relat_1, cc11_waybel_0, rc1_funct_1, dt_u1_orders_2, dt_l1_pre_topc, fc24_yellow_6, rc3_relat_1, t6_boole, rc2_subset_1, free_g1_pre_topc, rc2_waybel_7, rc5_tops_1, fc3_subset_1, t5_subset, existence_m1_relset_1, fc2_subset_1, rc3_waybel_7, rc4_funct_1, existence_m4_yellow_6, dt_l1_waybel_0, t2_tarski, rc4_tops_1, existence_l1_waybel_0, t4_subset, abstractness_v1_pre_topc, t7_boole, existence_l1_orders_2, cc1_funct_1, dt_g1_pre_topc, rc3_struct_0, fc1_subset_1, cc13_waybel_0, dt_g1_orders_2, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, commutativity_k2_tarski, fraenkel_a_2_1_yellow_6, fc1_finset_1, cc2_tops_1, rc2_relat_1, existence_m2_relset_1, free_g1_orders_2, fc1_struct_0, existence_l1_pre_topc, rc1_relat_1, reflexivity_r1_tarski, rc1_finset_1, rc2_tops_1, cc1_finset_1, cc7_yellow_6, t8_boole, dt_k3_waybel28, dt_u1_pre_topc, t2_subset, fc12_relat_1, rc5_struct_0, cc4_tops_1, cc2_lattice3, d10_xboole_0, fc2_finset_1
% 83.15/14.16 % No. of inferences in proof: 184
% 83.15/14.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13761 ms resp. 13246 ms w/o parsing
% 83.15/14.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.15/14.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------