TSTP Solution File: LAT292+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:27:24 EDT 2023
% Result : Theorem 5.62s 2.25s
% Output : Refutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 153
% Syntax : Number of formulae : 248 ( 19 unt; 60 typ; 0 def)
% Number of atoms : 911 ( 33 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 2383 ( 157 ~; 2 |; 538 &;1503 @)
% ( 4 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 60 usr; 2 con; 0-3 aty)
% Number of variables : 312 ( 0 ^; 252 !; 60 ?; 312 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(v2_pre_topc_type,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_type,type,
l1_pre_topc: $i > $o ).
thf(r1_filter_1_type,type,
r1_filter_1: $i > $i > $o ).
thf(k6_lopclset_type,type,
k6_lopclset: $i > $i ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(v4_finsub_1_type,type,
v4_finsub_1: $i > $o ).
thf(v1_finsub_1_type,type,
v1_finsub_1: $i > $o ).
thf(v3_finsub_1_type,type,
v3_finsub_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(g1_pre_topc_type,type,
g1_pre_topc: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(v1_pre_topc_type,type,
v1_pre_topc: $i > $o ).
thf(u1_pre_topc_type,type,
u1_pre_topc: $i > $i ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(v4_lattices_type,type,
v4_lattices: $i > $o ).
thf(v5_lattices_type,type,
v5_lattices: $i > $o ).
thf(v6_lattices_type,type,
v6_lattices: $i > $o ).
thf(v7_lattices_type,type,
v7_lattices: $i > $o ).
thf(v8_lattices_type,type,
v8_lattices: $i > $o ).
thf(v9_lattices_type,type,
v9_lattices: $i > $o ).
thf(k1_lopclset_type,type,
k1_lopclset: $i > $i ).
thf(k4_lopclset_type,type,
k4_lopclset: $i > $i ).
thf(k12_lopclset_type,type,
k12_lopclset: $i > $i ).
thf(k11_lopclset_type,type,
k11_lopclset: $i > $i ).
thf(v4_pre_topc_type,type,
v4_pre_topc: $i > $i > $o ).
thf(a_1_0_lopclset_type,type,
a_1_0_lopclset: $i > $i ).
thf(v3_pre_topc_type,type,
v3_pre_topc: $i > $i > $o ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(v12_lattices_type,type,
v12_lattices: $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(k5_lopclset_type,type,
k5_lopclset: $i > $i ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(142,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)],[16]) ).
thf(20,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(152,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)],[20]) ).
thf(77,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(403,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).
thf(339,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
=> ( r1_filter_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
thf(457,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
=> ( r1_filter_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(46,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(244,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(72,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).
thf(365,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(42,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(234,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(78,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).
thf(408,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(8,axiom,
! [A: $i] :
( ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) )
=> ( v4_finsub_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(115,plain,
! [A: $i] :
( ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) )
=> ( v4_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k1_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lopclset) ).
thf(276,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k1_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(88,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lopclset) ).
thf(449,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(73,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(379,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(202,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)],[34]) ).
thf(25,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(174,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(288,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(84,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ( v1_pre_topc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pre_topc) ).
thf(436,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ( v1_pre_topc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(50,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(257,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(110,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(70,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).
thf(344,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(216,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(86,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(443,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(66,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(321,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(5,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
thf(106,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(221,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(53,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
thf(265,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ( v3_pre_topc @ C @ B )
& ( v4_pre_topc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).
thf(312,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ( v3_pre_topc @ C @ B )
& ( v4_pre_topc @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ( v3_pre_topc @ C @ B )
& ( v4_pre_topc @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(35,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(206,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(117,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(85,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(439,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(3,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
thf(102,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(62,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_lopclset @ A )
= ( a_1_0_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lopclset) ).
thf(302,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_lopclset @ A )
= ( a_1_0_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(260,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)],[51]) ).
thf(81,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(429,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(137,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)],[14]) ).
thf(93,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(467,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(71,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k5_lopclset @ A ) )
& ( v1_funct_2 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lopclset) ).
thf(361,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k5_lopclset @ A ) )
& ( v1_funct_2 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(67,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).
thf(324,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(57,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k12_lopclset @ A )
= ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lopclset) ).
thf(285,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k12_lopclset @ A )
= ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(224,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)],[41]) ).
thf(61,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(298,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(148,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(176,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(79,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k6_lopclset @ A )
= ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lopclset) ).
thf(423,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k6_lopclset @ A )
= ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(191,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)],[30]) ).
thf(59,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
& ( v10_lattices @ ( k12_lopclset @ A ) )
& ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_lopclset) ).
thf(291,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
& ( v10_lattices @ ( k12_lopclset @ A ) )
& ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(87,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(445,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(144,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(236,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(187,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(172,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(219,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(89,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(451,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(83,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lopclset) ).
thf(434,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(213,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)],[37]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(198,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)],[32]) ).
thf(55,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k4_lopclset @ A ) )
& ( v1_funct_2 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lopclset) ).
thf(278,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k4_lopclset @ A ) )
& ( v1_funct_2 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(135,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)],[13]) ).
thf(45,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(241,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(167,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(80,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(426,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(7,axiom,
! [A: $i] :
( ( v4_finsub_1 @ A )
=> ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(112,plain,
! [A: $i] :
( ( v4_finsub_1 @ A )
=> ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(342,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)],[69]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(295,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(282,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)],[56]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lopclset) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
& ( v1_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v3_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(154,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
& ( v1_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v3_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(74,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_lopclset @ A ) )
& ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lopclset) ).
thf(386,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_lopclset @ A ) )
& ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(48,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_lopclset @ A ) )
& ( v10_lattices @ ( k6_lopclset @ A ) )
& ( l3_lattices @ ( k6_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lopclset) ).
thf(250,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_lopclset @ A ) )
& ( v10_lattices @ ( k6_lopclset @ A ) )
& ( l3_lattices @ ( k6_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(4,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(104,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(75,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
thf(390,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(15,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(139,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( ( v1_funct_1 @ ( u2_lattices @ A ) )
& ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(246,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( ( v1_funct_1 @ ( u2_lattices @ A ) )
& ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
? [A: $i] : ( l1_pre_topc @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(432,plain,
? [A: $i] : ( l1_pre_topc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(52,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(262,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(28,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( ( v1_funct_1 @ ( u1_lattices @ A ) )
& ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(183,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( ( v1_funct_1 @ ( u1_lattices @ A ) )
& ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(63,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) )
& ( l1_pre_topc @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_lopclset) ).
thf(305,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) )
& ( l1_pre_topc @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(44,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(239,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(126,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)],[11]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(400,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)],[76]) ).
thf(92,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(459,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(131,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)],[12]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(178,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)],[27]) ).
thf(22,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(163,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(200,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)],[33]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(254,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)],[49]) ).
thf(94,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lopclset) ).
thf(469,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(64,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(309,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(90,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(454,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(489,plain,
$false,
inference(e,[status(thm)],[142,152,403,339,457,244,365,234,408,115,276,449,379,202,174,288,436,257,110,344,196,216,443,321,106,221,265,312,206,117,439,102,302,260,429,137,467,361,324,285,224,298,148,176,423,191,291,445,144,236,187,172,219,451,434,208,213,198,278,135,241,167,426,112,342,295,282,150,95,154,386,250,104,390,139,119,246,432,262,183,305,239,126,400,459,131,178,163,200,254,469,309,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.08 % Problem : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.11 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 14:20:35 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.64/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.83 % [INFO] Parsing done (153ms).
% 0.88/0.84 % [INFO] Running in sequential loop mode.
% 1.44/1.05 % [INFO] eprover registered as external prover.
% 1.44/1.05 % [INFO] cvc4 registered as external prover.
% 1.44/1.05 % [INFO] Scanning for conjecture ...
% 1.59/1.14 % [INFO] Found a conjecture and 111 axioms. Running axiom selection ...
% 1.87/1.21 % [INFO] Axiom selection finished. Selected 92 axioms (removed 19 axioms).
% 2.09/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.31 % [INFO] Type checking passed.
% 2.26/1.31 % [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 ...
% 5.62/2.25 % External prover 'e' found a proof!
% 5.62/2.25 % [INFO] Killing All external provers ...
% 5.62/2.25 % Time passed: 1858ms (effective reasoning time: 1404ms)
% 5.62/2.25 % 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)>
% 5.62/2.25 % Axioms used in derivation (92): redefinition_m2_relset_1, cc2_finset_1, existence_l3_lattices, rc1_lopclset, d9_lopclset, cc18_membered, cc3_lattices, existence_m2_relset_1, fc1_finsub_1, rc4_finset_1, symmetry_r1_filter_1, rc12_lattices, cc6_lattices, existence_l1_lattices, t1_subset, rc2_partfun1, cc4_lattices, dt_m2_relset_1, reflexivity_r1_filter_1, dt_k4_lopclset, d4_lopclset, cc2_finsub_1, rc6_pre_topc, dt_k6_lopclset, dt_k12_lopclset, rc11_lattices, rc3_lattices, dt_l1_lattices, dt_l1_pre_topc, t6_boole, existence_l2_lattices, dt_k1_lopclset, fc4_lopclset, free_g1_pre_topc, dt_k11_lopclset, t5_subset, existence_m1_relset_1, dt_l3_lattices, dt_l2_lattices, t2_tarski, rc13_lattices, cc5_lattices, t4_subset, cc1_funct_2, abstractness_v1_pre_topc, t7_boole, dt_g1_pre_topc, rc3_struct_0, cc4_membered, cc1_lattices, rc1_funct_2, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, cc1_finsub_1, fc1_struct_0, cc6_funct_2, existence_l1_pre_topc, fc1_lopclset, reflexivity_r1_tarski, cc17_membered, dt_g3_lattices, fraenkel_a_1_0_lopclset, rc1_pre_topc, rc6_lattices, rc7_pre_topc, free_g3_lattices, cc7_lattices, dt_k5_lopclset, rc3_finset_1, rc1_finset_1, d1_lopclset, cc1_finset_1, abstractness_v3_lattices, t8_boole, dt_u1_pre_topc, rc5_struct_0, t2_subset, cc3_membered, rc2_pre_topc, existence_l1_struct_0, rc10_lattices, cc5_funct_2, dt_u2_lattices, fc14_finset_1, cc16_membered, fc3_lattices, antisymmetry_r2_hidden, t43_lopclset, cc2_lattices
% 5.62/2.25 % No. of inferences in proof: 188
% 5.62/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1858 ms resp. 1404 ms w/o parsing
% 5.83/2.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.83/2.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------