TSTP Solution File: LAT284+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT284+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:27:19 EDT 2023
% Result : Theorem 8.60s 2.91s
% Output : Refutation 8.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 191
% Syntax : Number of formulae : 320 ( 29 unt; 64 typ; 0 def)
% Number of atoms : 1042 ( 58 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 3141 ( 131 ~; 2 |; 514 &;2224 @)
% ( 5 <=>; 265 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 2 con; 0-6 aty)
% Number of variables : 506 ( 0 ^; 459 !; 47 ?; 506 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v2_pre_topc_type,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_type,type,
l1_pre_topc: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k6_lopclset_type,type,
k6_lopclset: $i > $i ).
thf(k4_lattices_type,type,
k4_lattices: $i > $i > $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
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_xcmplx_0_type,type,
v1_xcmplx_0: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $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(v1_rat_1_type,type,
v1_rat_1: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_xreal_0_type,type,
v1_xreal_0: $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(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v4_ordinal2_type,type,
v4_ordinal2: $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_lopclset_type,type,
k1_lopclset: $i > $i ).
thf(k3_lopclset_type,type,
k3_lopclset: $i > $i > $i > $i ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(v6_lattices_type,type,
v6_lattices: $i > $o ).
thf(m2_subset_1_type,type,
m2_subset_1: $i > $i > $i > $o ).
thf(v4_lattices_type,type,
v4_lattices: $i > $o ).
thf(v5_lattices_type,type,
v5_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(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(k4_lopclset_type,type,
k4_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(k2_lattices_type,type,
k2_lattices: $i > $i > $i > $i ).
thf(v3_pre_topc_type,type,
v3_pre_topc: $i > $i > $o ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k5_lopclset_type,type,
k5_lopclset: $i > $i ).
thf(83,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(418,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',dt_k5_lopclset) ).
thf(518,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)],[104]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(481,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(63,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(352,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(13,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(170,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(217,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',dt_k1_lopclset) ).
thf(379,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)],[70]) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(385,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)],[72]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc27_membered) ).
thf(533,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(60,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(340,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(18,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(185,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(320,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc32_membered) ).
thf(436,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(174,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(404,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(504,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)],[101]) ).
thf(123,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(587,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(9,axiom,
! [A: $i] :
( ( v1_rat_1 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_membered) ).
thf(157,plain,
! [A: $i] :
( ( v1_rat_1 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(112,axiom,
? [A: $i] : ( l1_pre_topc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(542,plain,
? [A: $i] : ( l1_pre_topc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(460,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)],[90]) ).
thf(84,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(421,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc29_membered) ).
thf(606,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(44,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(284,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(416,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc35_membered) ).
thf(443,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v5_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( v4_ordinal2 @ A )
& ( v4_ordinal2 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) )
& ( v4_membered @ ( k2_tarski @ A @ B ) )
& ( v5_membered @ ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_membered) ).
thf(253,plain,
! [A: $i,B: $i] :
( ( ( v4_ordinal2 @ A )
& ( v4_ordinal2 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) )
& ( v4_membered @ ( k2_tarski @ A @ B ) )
& ( v5_membered @ ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(485,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)],[96]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(348,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)],[62]) ).
thf(126,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(602,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(106,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(527,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(50,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(312,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(46,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(292,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) )
& ( v4_membered @ ( k1_tarski @ A ) )
& ( v5_membered @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_membered) ).
thf(233,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) )
& ( v4_membered @ ( k1_tarski @ A ) )
& ( v5_membered @ ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(34,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k1_binop_1 @ A @ B @ C )
= ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(248,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k1_binop_1 @ A @ B @ C )
= ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(512,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(546,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(20,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(201,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)],[20]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',dt_k4_lopclset) ).
thf(381,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)],[71]) ).
thf(40,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(270,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(529,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(57,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(334,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(302,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)],[49]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(165,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)],[11]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(192,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)],[19]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k2_lattices @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(407,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k2_lattices @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(42,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(275,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc30_membered) ).
thf(522,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(27,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(224,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(388,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)],[73]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(356,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)],[64]) ).
thf(100,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(499,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(590,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_subset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( v1_xreal_0 @ A )
& ( v1_xreal_0 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_membered) ).
thf(212,plain,
! [A: $i,B: $i] :
( ( ( v1_xreal_0 @ A )
& ( v1_xreal_0 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(89,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(457,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k4_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lopclset) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k4_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(129,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k4_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(67,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(371,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)],[67]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).
thf(360,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)],[66]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(205,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)],[21]) ).
thf(76,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(398,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)],[76]) ).
thf(7,axiom,
! [A: $i] :
( ( v1_xcmplx_0 @ A )
=> ( v1_membered @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_membered) ).
thf(148,plain,
! [A: $i] :
( ( v1_xcmplx_0 @ A )
=> ( v1_membered @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(161,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(562,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(16,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) )
& ( v4_membered @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_membered) ).
thf(176,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) )
& ( v3_membered @ ( k1_tarski @ A ) )
& ( v4_membered @ ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(77,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(402,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)],[77]) ).
thf(37,axiom,
! [A: $i] :
( ( v1_xreal_0 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_membered) ).
thf(259,plain,
! [A: $i] :
( ( v1_xreal_0 @ A )
=> ( ( v1_membered @ ( k1_tarski @ A ) )
& ( v2_membered @ ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lopclset) ).
thf(413,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(74,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(391,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)],[74]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc33_membered) ).
thf(572,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v4_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(128,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(611,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( v1_rat_1 @ A )
& ( v1_rat_1 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_membered) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( v1_rat_1 @ A )
& ( v1_rat_1 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(219,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)],[26]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(377,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)],[69]) ).
thf(29,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(230,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(318,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)],[52]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(483,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(35,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(251,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',dt_k6_lopclset) ).
thf(330,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)],[56]) ).
thf(48,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(299,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(241,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(108,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(531,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)],[108]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(374,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)],[68]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(487,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)],[97]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(150,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)],[8]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_lopclset @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lopclset) ).
thf(327,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_lopclset @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(585,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(59,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(338,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)],[59]) ).
thf(113,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lopclset) ).
thf(544,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)],[113]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(314,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)],[51]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc31_membered) ).
thf(595,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v2_membered @ ( k3_xboole_0 @ A @ B ) )
& ( v3_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(5,axiom,
! [A: $i] :
( ( v4_finsub_1 @ A )
=> ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(143,plain,
! [A: $i] :
( ( v4_finsub_1 @ A )
=> ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(465,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)],[91]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(539,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)],[111]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(581,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)],[121]) ).
thf(119,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( k2_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) @ B @ C )
= ( k3_lopclset @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lopclset) ).
thf(568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( k2_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) @ B @ C )
= ( k3_lopclset @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(33,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(246,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(93,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(478,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)],[93]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( m2_subset_1 @ ( k3_lopclset @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lopclset) ).
thf(346,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( m2_subset_1 @ ( k3_lopclset @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v5_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc36_membered) ).
thf(549,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v5_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',d4_lopclset) ).
thf(536,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)],[110]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(287,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)],[45]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(410,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)],[80]) ).
thf(6,axiom,
! [A: $i] :
( ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) )
=> ( v4_finsub_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(146,plain,
! [A: $i] :
( ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) )
=> ( v4_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(273,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(168,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(38,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(262,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_lopclset) ).
thf(564,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(22,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(210,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(239,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( v1_int_1 @ A )
& ( v1_int_1 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) )
& ( v4_membered @ ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_membered) ).
thf(294,plain,
! [A: $i,B: $i] :
( ( ( v1_int_1 @ A )
& ( v1_int_1 @ B ) )
=> ( ( v1_membered @ ( k2_tarski @ A @ B ) )
& ( v2_membered @ ( k2_tarski @ A @ B ) )
& ( v3_membered @ ( k2_tarski @ A @ B ) )
& ( v4_membered @ ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( v1_xcmplx_0 @ A )
& ( v1_xcmplx_0 @ B ) )
=> ( v1_membered @ ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_membered) ).
thf(268,plain,
! [A: $i,B: $i] :
( ( ( v1_xcmplx_0 @ A )
& ( v1_xcmplx_0 @ B ) )
=> ( v1_membered @ ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(358,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)],[65]) ).
thf(75,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_lopclset @ A )
= ( a_1_0_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lopclset) ).
thf(395,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)],[75]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc34_membered) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v2_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v3_membered @ ( k3_xboole_0 @ B @ A ) )
& ( v4_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(43,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(277,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(227,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)],[28]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(322,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).
thf(469,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)],[92]) ).
thf(24,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(215,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(116,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(560,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(98,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(491,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(496,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc28_membered) ).
thf(454,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(628,plain,
$false,
inference(cvc4,[status(thm)],[418,518,481,352,170,217,379,385,533,340,185,320,436,174,404,504,587,157,542,460,421,606,284,416,443,253,485,348,602,527,312,292,233,248,512,546,201,381,270,529,334,302,165,192,407,275,137,522,224,388,356,499,590,212,515,457,129,371,360,205,398,148,161,562,176,402,259,413,391,572,611,181,172,219,377,230,318,140,483,251,330,299,241,531,374,487,150,327,585,338,544,336,314,595,143,465,539,581,568,246,478,346,549,536,287,410,146,273,168,262,564,210,239,294,268,358,395,427,277,227,322,469,215,560,491,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LAT284+1 : TPTP v8.1.2. Released v3.4.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n022.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 14:22:33 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.06 % [INFO] Parsing done (184ms).
% 1.47/1.07 % [INFO] Running in sequential loop mode.
% 1.93/1.27 % [INFO] eprover registered as external prover.
% 1.93/1.27 % [INFO] cvc4 registered as external prover.
% 1.93/1.28 % [INFO] Scanning for conjecture ...
% 2.23/1.36 % [INFO] Found a conjecture and 139 axioms. Running axiom selection ...
% 2.23/1.45 % [INFO] Axiom selection finished. Selected 126 axioms (removed 13 axioms).
% 2.89/1.55 % [INFO] Problem is first-order (TPTP FOF).
% 2.89/1.56 % [INFO] Type checking passed.
% 2.89/1.57 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.60/2.91 % External prover 'cvc4' found a proof!
% 8.60/2.91 % [INFO] Killing All external provers ...
% 8.60/2.91 % Time passed: 2376ms (effective reasoning time: 1841ms)
% 8.60/2.91 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.60/2.91 % Axioms used in derivation (126): redefinition_m2_relset_1, cc18_membered, redefinition_k2_binop_1, cc12_membered, cc2_finset_1, idempotence_k3_lopclset, fc1_finsub_1, idempotence_k3_xboole_0, rc4_finset_1, cc10_membered, existence_l1_lattices, d5_tarski, t1_subset, fc34_membered, fc31_membered, existence_l3_lattices, rc1_membered, t2_boole, fc9_membered, redefinition_k3_lopclset, rc2_partfun1, t6_lopclset, fc7_membered, dt_m2_relset_1, commutativity_k3_xboole_0, fc28_membered, dt_k4_lopclset, fc11_finset_1, d4_lopclset, dt_k2_binop_1, cc2_finsub_1, rc6_pre_topc, fc32_membered, fc30_membered, dt_k6_lopclset, rc3_lattices, dt_l1_lattices, commutativity_k3_lopclset, dt_l1_pre_topc, fc10_finset_1, fc15_membered, t6_boole, dt_k1_lopclset, existence_l2_lattices, fc33_membered, fc16_membered, t5_subset, cc19_membered, existence_m1_relset_1, dt_l3_lattices, fc11_membered, dt_l2_lattices, fc6_membered, t2_tarski, cc11_membered, t4_subset, cc1_funct_2, cc20_membered, t7_boole, fc10_membered, rc3_struct_0, commutativity_k4_lattices, fc29_membered, cc4_membered, cc1_lattices, rc1_funct_2, t3_subset, cc1_relset_1, cc13_membered, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, commutativity_k2_tarski, cc15_membered, fc1_finset_1, existence_m2_subset_1, existence_m2_relset_1, fc13_membered, fc14_membered, cc1_finsub_1, fc1_struct_0, cc6_funct_2, existence_l1_pre_topc, fc1_lopclset, dt_k4_lattices, fc35_membered, reflexivity_r1_tarski, fc8_membered, fc36_membered, cc17_membered, d2_lattices, dt_g3_lattices, fraenkel_a_1_0_lopclset, rc6_lattices, rc7_pre_topc, free_g3_lattices, dt_k5_lopclset, rc3_finset_1, dt_m2_subset_1, rc1_finset_1, d1_lopclset, cc1_finset_1, abstractness_v3_lattices, t8_boole, rc5_struct_0, t2_subset, cc1_membered, cc2_membered, fc12_membered, cc3_membered, fc2_finset_1, cc14_membered, existence_l1_struct_0, dt_k2_lattices, cc5_funct_2, redefinition_m2_subset_1, dt_u2_lattices, fc14_finset_1, cc16_membered, dt_k3_lopclset, d1_binop_1, fc27_membered, fc3_lattices, antisymmetry_r2_hidden, cc2_lattices, redefinition_k4_lattices
% 8.60/2.91 % No. of inferences in proof: 256
% 8.60/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2376 ms resp. 1841 ms w/o parsing
% 8.60/2.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.60/2.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------