%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT292+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:00 AM UTC 2026
% Result : Theorem 4.40s 2.07s
% Output : Refutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 93
% Syntax : Number of formulae : 188 ( 19 unt; 0 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 : 0 ( 0 >; 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_decl,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_decl,type,
v10_lattices: $i > $o ).
thf(v17_lattices_decl,type,
v17_lattices: $i > $o ).
thf(v3_realset2_decl,type,
v3_realset2: $i > $o ).
thf(l3_lattices_decl,type,
l3_lattices: $i > $o ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_decl,type,
l1_pre_topc: $i > $o ).
thf(r1_filter_1_decl,type,
r1_filter_1: $i > $i > $o ).
thf(k6_lopclset_decl,type,
k6_lopclset: $i > $i ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v4_finsub_1_decl,type,
v4_finsub_1: $i > $o ).
thf(v1_finsub_1_decl,type,
v1_finsub_1: $i > $o ).
thf(v3_finsub_1_decl,type,
v3_finsub_1: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(g1_pre_topc_decl,type,
g1_pre_topc: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(u2_lattices_decl,type,
u2_lattices: $i > $i ).
thf(v1_pre_topc_decl,type,
v1_pre_topc: $i > $o ).
thf(u1_pre_topc_decl,type,
u1_pre_topc: $i > $i ).
thf(v13_lattices_decl,type,
v13_lattices: $i > $o ).
thf(v14_lattices_decl,type,
v14_lattices: $i > $o ).
thf(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(v4_lattices_decl,type,
v4_lattices: $i > $o ).
thf(v5_lattices_decl,type,
v5_lattices: $i > $o ).
thf(v6_lattices_decl,type,
v6_lattices: $i > $o ).
thf(v7_lattices_decl,type,
v7_lattices: $i > $o ).
thf(v8_lattices_decl,type,
v8_lattices: $i > $o ).
thf(v9_lattices_decl,type,
v9_lattices: $i > $o ).
thf(k1_lopclset_decl,type,
k1_lopclset: $i > $i ).
thf(k4_lopclset_decl,type,
k4_lopclset: $i > $i ).
thf(k12_lopclset_decl,type,
k12_lopclset: $i > $i ).
thf(k11_lopclset_decl,type,
k11_lopclset: $i > $i ).
thf(v4_pre_topc_decl,type,
v4_pre_topc: $i > $i > $o ).
thf(a_1_0_lopclset_decl,type,
a_1_0_lopclset: $i > $i ).
thf(v3_pre_topc_decl,type,
v3_pre_topc: $i > $i > $o ).
thf(v11_lattices_decl,type,
v11_lattices: $i > $o ).
thf(v12_lattices_decl,type,
v12_lattices: $i > $o ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(k5_lopclset_decl,type,
k5_lopclset: $i > $i ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ v1_funct_2 ) ) )
& ( A @ k4_lopclset @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lopclset) ).
thf(301,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ v1_funct_2 ) ) )
& ( A @ k4_lopclset @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ l3_lattices )
& ( A @ k6_lopclset @ v10_lattices )
& ~ ( A @ k6_lopclset @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lopclset) ).
thf(270,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ l3_lattices )
& ( A @ k6_lopclset @ v10_lattices )
& ~ ( A @ k6_lopclset @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(503,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(509,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(78,axiom,
? [A: $i] :
( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).
thf(450,plain,
? [A: $i] :
( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(83,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_lopclset @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lopclset) ).
thf(479,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_lopclset @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(93,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(518,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(84,axiom,
? [A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pre_topc) ).
thf(481,plain,
? [A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(120,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g1_pre_topc ) @ l1_pre_topc )
& ( B @ ( A @ g1_pre_topc ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(440,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g1_pre_topc ) @ l1_pre_topc )
& ( B @ ( A @ g1_pre_topc ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(184,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(67,axiom,
? [A: $i] :
( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).
thf(357,plain,
? [A: $i] :
( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ v3_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(284,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ v3_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(416,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(216,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(492,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ u1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(376,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ u1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(85,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(485,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(66,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(353,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(35,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(221,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ v1_funct_2 ) ) )
& ( A @ k5_lopclset @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lopclset) ).
thf(396,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ v1_funct_2 ) ) )
& ( A @ k5_lopclset @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(265,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
=> ( A @ ( B @ r1_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
thf(507,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
=> ( A @ ( B @ r1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ l1_pre_topc )
& ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_lopclset) ).
thf(334,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ l1_pre_topc )
& ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(45,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(260,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(74,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc )
& ~ ( A @ k11_lopclset @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lopclset) ).
thf(424,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc )
& ~ ( A @ k11_lopclset @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_lattices) ).
thf(429,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_pre_topc )
=> ( A
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(275,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_pre_topc )
=> ( A
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(229,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(252,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(59,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset @ l3_lattices )
& ( A @ k12_lopclset @ v10_lattices )
& ~ ( A @ k12_lopclset @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_lopclset) ).
thf(317,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset @ l3_lattices )
& ( A @ k12_lopclset @ v10_lattices )
& ~ ( A @ k12_lopclset @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(188,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(499,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(64,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(339,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(212,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(105,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(40,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(237,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v4_finsub_1 )
& ( A @ k1_zfmisc_1 @ v3_finsub_1 )
& ( A @ k1_zfmisc_1 @ v1_finsub_1 )
& ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(161,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v4_finsub_1 )
& ( A @ k1_zfmisc_1 @ v3_finsub_1 )
& ( A @ k1_zfmisc_1 @ v1_finsub_1 )
& ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(77,axiom,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(444,plain,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(176,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ v3_finsub_1 )
& ( A @ v1_finsub_1 ) )
=> ( A @ v4_finsub_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(118,plain,
! [A: $i] :
( ( ( A @ v3_finsub_1 )
& ( A @ v1_finsub_1 ) )
=> ( A @ v4_finsub_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(204,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(313,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset )
= ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lopclset) ).
thf(466,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset )
= ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(159,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(82,axiom,
? [A: $i] : ( A @ l1_pre_topc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(477,plain,
? [A: $i] : ( A @ l1_pre_topc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(103,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(94,axiom,
? [A: $i] :
( ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lopclset) ).
thf(520,plain,
? [A: $i] :
( ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(155,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(278,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(223,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(56,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(306,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(54,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_lopclset @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lopclset) ).
thf(299,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_lopclset @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(241,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(473,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(490,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(112,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(194,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(145,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(282,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lopclset) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,plain,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(263,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(57,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset )
= ( A @ k11_lopclset @ k6_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lopclset) ).
thf(310,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset )
= ( A @ k11_lopclset @ k6_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(199,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(182,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset )
= ( A @ a_1_0_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lopclset) ).
thf(331,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset )
= ( A @ a_1_0_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(88,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ r1_filter_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lopclset) ).
thf(497,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ r1_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(44,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(258,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(186,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ v4_finsub_1 )
=> ( ( A @ v3_finsub_1 )
& ( A @ v1_finsub_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(114,plain,
! [A: $i] :
( ( A @ v4_finsub_1 )
=> ( ( A @ v3_finsub_1 )
& ( A @ v1_finsub_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(72,axiom,
? [A: $i] :
( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).
thf(401,plain,
? [A: $i] :
( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(22,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(171,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(70,axiom,
? [A: $i] :
( ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).
thf(378,plain,
? [A: $i] :
( ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(235,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(214,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,axiom,
? [A: $i] :
( ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).
thf(287,plain,
? [A: $i] :
( ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(151,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r1_filter_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).
thf(373,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r1_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(136,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(326,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(107,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(254,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(322,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(122,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(80,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(469,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(232,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(539,plain,
$false,
inference(e,[status(thm)],[301,270,503,509,450,479,518,481,120,440,184,357,157,284,416,216,492,376,485,353,221,396,265,507,334,260,424,429,275,229,252,317,188,141,499,339,212,105,343,237,161,444,149,176,118,204,313,466,159,477,103,520,155,130,278,223,306,299,241,473,490,112,194,145,282,95,263,310,199,182,331,143,497,258,186,114,401,171,378,235,214,287,151,373,210,136,326,107,254,322,122,469,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT292+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.38 % Computer : n012.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 20:30:35 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.60/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.99/0.92 % [INFO] Parsing done (140ms).
% 0.99/0.92 % [INFO] Running in sequential loop mode.
% 1.51/1.12 % [INFO] eprover registered as external prover.
% 1.51/1.13 % [INFO] Scanning for conjecture ...
% 1.66/1.20 % [INFO] Found a conjecture (or negated_conjecture) and 111 axioms. Running axiom selection ...
% 1.66/1.27 % [INFO] Axiom selection finished. Selected 92 axioms (removed 19 axioms).
% 2.00/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.00/1.35 % [INFO] Type checking passed.
% 2.00/1.35 % [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 ...
% 4.40/2.06 % External prover 'e' found a proof!
% 4.40/2.06 % [INFO] Killing All external provers ...
% 4.40/2.06 % Time passed: 1563ms (effective reasoning time: 1137ms)
% 4.40/2.06 % 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)>
% 4.40/2.06 % 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
% 4.40/2.06 % No. of inferences in proof: 188
% 4.40/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1563 ms resp. 1137 ms w/o parsing
% 4.78/2.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.78/2.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------