TSTP Solution File: LAT338+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT338+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:27:58 EDT 2023
% Result : Theorem 6.36s 2.59s
% Output : Refutation 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 154
% Syntax : Number of formulae : 251 ( 29 unt; 59 typ; 0 def)
% Number of atoms : 827 ( 35 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 2606 ( 170 ~; 2 |; 448 &;1801 @)
% ( 5 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 2 con; 0-3 aty)
% Number of variables : 342 ( 0 ^; 279 !; 63 ?; 342 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_conlat_1_type,type,
v3_conlat_1: $i > $o ).
thf(l2_conlat_1_type,type,
l2_conlat_1: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k11_conlat_1_type,type,
k11_conlat_1: $i > $i ).
thf(v7_conlat_1_type,type,
v7_conlat_1: $i > $i > $o ).
thf(k16_lattice3_type,type,
k16_lattice3: $i > $i > $i ).
thf(v9_conlat_1_type,type,
v9_conlat_1: $i > $i > $o ).
thf(l3_conlat_1_type,type,
l3_conlat_1: $i > $i > $o ).
thf(k15_lattice3_type,type,
k15_lattice3: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(v4_lattices_type,type,
v4_lattices: $i > $o ).
thf(v5_lattices_type,type,
v5_lattices: $i > $o ).
thf(v6_lattices_type,type,
v6_lattices: $i > $o ).
thf(v7_lattices_type,type,
v7_lattices: $i > $o ).
thf(v8_lattices_type,type,
v8_lattices: $i > $o ).
thf(v9_lattices_type,type,
v9_lattices: $i > $o ).
thf(v10_lattices_type,type,
v10_lattices: $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(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(l1_conlat_1_type,type,
l1_conlat_1: $i > $o ).
thf(v6_conlat_1_type,type,
v6_conlat_1: $i > $i > $o ).
thf(k10_conlat_1_type,type,
k10_conlat_1: $i > $i ).
thf(k8_conlat_1_type,type,
k8_conlat_1: $i > $i ).
thf(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(u2_conlat_1_type,type,
u2_conlat_1: $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(u1_conlat_1_type,type,
u1_conlat_1: $i > $i ).
thf(m1_conlat_1_type,type,
m1_conlat_1: $i > $i > $o ).
thf(a_2_1_lattice3_type,type,
a_2_1_lattice3: $i > $i > $i ).
thf(r3_lattice3_type,type,
r3_lattice3: $i > $i > $i > $o ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(g3_conlat_1_type,type,
g3_conlat_1: $i > $i > $i > $i ).
thf(u4_conlat_1_type,type,
u4_conlat_1: $i > $i > $i ).
thf(u5_conlat_1_type,type,
u5_conlat_1: $i > $i > $i ).
thf(k7_conlat_1_type,type,
k7_conlat_1: $i > $i ).
thf(v8_conlat_1_type,type,
v8_conlat_1: $i > $i > $o ).
thf(v4_lattice3_type,type,
v4_lattice3: $i > $o ).
thf(k9_conlat_1_type,type,
k9_conlat_1: $i > $i ).
thf(22,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(169,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)],[22]) ).
thf(18,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(155,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(64,axiom,
! [A: $i] :
( ( l2_conlat_1 @ A )
=> ( l1_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_conlat_1) ).
thf(342,plain,
! [A: $i] :
( ( l2_conlat_1 @ A )
=> ( l1_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(13,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(139,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)],[13]) ).
thf(80,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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',fc3_lattice2) ).
thf(408,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[80]) ).
thf(58,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_conlat_1) ).
thf(308,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(41,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_conlat_1) ).
thf(247,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(379,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(49,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(269,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)],[49]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_conlat_1 @ A @ B @ C )
= ( g3_conlat_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_conlat_1) ).
thf(385,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_conlat_1 @ A @ B @ C )
= ( g3_conlat_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(153,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(174,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(185,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(62,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k8_conlat_1 @ A ) )
<=> ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_conlat_1) ).
thf(320,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ ( k8_conlat_1 @ A ) )
=> ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) ) )
& ( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( r2_hidden @ B @ ( k8_conlat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u4_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u4_conlat_1) ).
thf(436,plain,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u4_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(65,axiom,
? [A: $i] : ( l2_conlat_1 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_conlat_1) ).
thf(344,plain,
? [A: $i] : ( l2_conlat_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(19,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(157,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)],[19]) ).
thf(28,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(189,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(82,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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',fc4_lattice2) ).
thf(416,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[82]) ).
thf(46,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(261,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)],[46]) ).
thf(34,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(216,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(238,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(68,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(353,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)],[68]) ).
thf(52,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_conlat_1) ).
thf(280,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(94,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_conlat_1) ).
thf(453,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(10,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(132,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(312,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(33,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(206,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)],[33]) ).
thf(74,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] : ( m1_conlat_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_conlat_1) ).
thf(381,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] : ( m1_conlat_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(3,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(102,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(67,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( l3_lattices @ ( k11_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_conlat_1) ).
thf(349,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( l3_lattices @ ( k11_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(77,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattices @ ( k11_conlat_1 @ A ) )
& ( v5_lattices @ ( k11_conlat_1 @ A ) )
& ( v6_lattices @ ( k11_conlat_1 @ A ) )
& ( v7_lattices @ ( k11_conlat_1 @ A ) )
& ( v8_lattices @ ( k11_conlat_1 @ A ) )
& ( v9_lattices @ ( k11_conlat_1 @ A ) )
& ( v10_lattices @ ( k11_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_conlat_1) ).
thf(392,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattices @ ( k11_conlat_1 @ A ) )
& ( v5_lattices @ ( k11_conlat_1 @ A ) )
& ( v6_lattices @ ( k11_conlat_1 @ A ) )
& ( v7_lattices @ ( k11_conlat_1 @ A ) )
& ( v8_lattices @ ( k11_conlat_1 @ A ) )
& ( v9_lattices @ ( k11_conlat_1 @ A ) )
& ( v10_lattices @ ( k11_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(192,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(165,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(43,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v1_funct_1 @ ( k10_conlat_1 @ A ) )
& ( v1_funct_2 @ ( k10_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) )
& ( m2_relset_1 @ ( k10_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_conlat_1) ).
thf(252,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v1_funct_1 @ ( k10_conlat_1 @ A ) )
& ( v1_funct_2 @ ( k10_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) )
& ( m2_relset_1 @ ( k10_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_conlat_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(97,plain,
~ ! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_1_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattice3 @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice3) ).
thf(285,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattice3 @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattice3 @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_1_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(37,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).
thf(224,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,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(193,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)],[30]) ).
thf(44,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(256,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattices @ ( k11_conlat_1 @ A ) )
& ( v5_lattices @ ( k11_conlat_1 @ A ) )
& ( v6_lattices @ ( k11_conlat_1 @ A ) )
& ( v7_lattices @ ( k11_conlat_1 @ A ) )
& ( v8_lattices @ ( k11_conlat_1 @ A ) )
& ( v9_lattices @ ( k11_conlat_1 @ A ) )
& ( v10_lattices @ ( k11_conlat_1 @ A ) )
& ( v13_lattices @ ( k11_conlat_1 @ A ) )
& ( v14_lattices @ ( k11_conlat_1 @ A ) )
& ( v15_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattice3 @ ( k11_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_conlat_2) ).
thf(328,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattices @ ( k11_conlat_1 @ A ) )
& ( v5_lattices @ ( k11_conlat_1 @ A ) )
& ( v6_lattices @ ( k11_conlat_1 @ A ) )
& ( v7_lattices @ ( k11_conlat_1 @ A ) )
& ( v8_lattices @ ( k11_conlat_1 @ A ) )
& ( v9_lattices @ ( k11_conlat_1 @ A ) )
& ( v10_lattices @ ( k11_conlat_1 @ A ) )
& ( v13_lattices @ ( k11_conlat_1 @ A ) )
& ( v14_lattices @ ( k11_conlat_1 @ A ) )
& ( v15_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattice3 @ ( k11_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(96,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(457,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)],[96]) ).
thf(9,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(129,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)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(48,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_conlat_1) ).
thf(266,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_conlat_1) ).
thf(425,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(15,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(148,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(180,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(91,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_conlat_1) ).
thf(444,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v1_funct_1 @ ( k9_conlat_1 @ A ) )
& ( v1_funct_2 @ ( k9_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) )
& ( m2_relset_1 @ ( k9_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_conlat_1) ).
thf(375,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v1_funct_1 @ ( k9_conlat_1 @ A ) )
& ( v1_funct_2 @ ( k9_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) )
& ( m2_relset_1 @ ( k9_conlat_1 @ A ) @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ A ) @ ( k8_conlat_1 @ A ) ) @ ( k8_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(78,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ( v8_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_conlat_1) ).
thf(402,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ( v8_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(45,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(259,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)],[45]) ).
thf(79,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_conlat_1) ).
thf(406,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(51,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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',fc5_lattice2) ).
thf(274,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[51]) ).
thf(70,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattices @ ( k11_conlat_1 @ A ) )
& ( v5_lattices @ ( k11_conlat_1 @ A ) )
& ( v6_lattices @ ( k11_conlat_1 @ A ) )
& ( v7_lattices @ ( k11_conlat_1 @ A ) )
& ( v8_lattices @ ( k11_conlat_1 @ A ) )
& ( v9_lattices @ ( k11_conlat_1 @ A ) )
& ( v10_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattice3 @ ( k11_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_conlat_1) ).
thf(362,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_conlat_1 @ A ) )
& ( v3_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattices @ ( k11_conlat_1 @ A ) )
& ( v5_lattices @ ( k11_conlat_1 @ A ) )
& ( v6_lattices @ ( k11_conlat_1 @ A ) )
& ( v7_lattices @ ( k11_conlat_1 @ A ) )
& ( v8_lattices @ ( k11_conlat_1 @ A ) )
& ( v9_lattices @ ( k11_conlat_1 @ A ) )
& ( v10_lattices @ ( k11_conlat_1 @ A ) )
& ( v4_lattice3 @ ( k11_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(40,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(245,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(61,axiom,
! [A: $i] :
( ( ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( v8_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_conlat_1) ).
thf(318,plain,
! [A: $i] :
( ( ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( v8_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(87,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(434,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)],[87]) ).
thf(50,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(271,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)],[50]) ).
thf(95,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_conlat_1) ).
thf(455,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(56,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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',fc2_lattice2) ).
thf(299,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[56]) ).
thf(89,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k16_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_1_lattice3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d22_lattice3) ).
thf(438,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k16_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_1_lattice3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ( ( v6_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_conlat_1) ).
thf(431,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ( ( v6_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(39,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(241,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(21,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(167,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,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(150,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)],[16]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u5_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u5_conlat_1) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u5_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(47,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(263,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)],[47]) ).
thf(24,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(177,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)],[24]) ).
thf(90,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(441,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(92,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_conlat_1) ).
thf(446,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(14,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(143,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)],[14]) ).
thf(42,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(250,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(450,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(32,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(203,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(35,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(218,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)],[35]) ).
thf(4,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(104,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)],[4]) ).
thf(75,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(383,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)],[75]) ).
thf(66,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k11_conlat_1 @ A )
= ( g3_lattices @ ( k8_conlat_1 @ A ) @ ( k10_conlat_1 @ A ) @ ( k9_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d23_conlat_1) ).
thf(346,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k11_conlat_1 @ A )
= ( g3_lattices @ ( k8_conlat_1 @ A ) @ ( k10_conlat_1 @ A ) @ ( k9_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(60,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k8_conlat_1 @ A )
= ( k7_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_conlat_1) ).
thf(315,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k8_conlat_1 @ A )
= ( k7_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(26,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(183,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(83,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(422,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(71,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] : ( l3_conlat_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_conlat_1) ).
thf(373,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] : ( l3_conlat_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ B @ A )
=> ( B
= ( g3_conlat_1 @ A @ ( u4_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v6_conlat_1) ).
thf(305,plain,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ B @ A )
=> ( B
= ( g3_conlat_1 @ A @ ( u4_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(69,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(358,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)],[69]) ).
thf(53,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_conlat_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_conlat_1) ).
thf(283,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_conlat_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(55,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc14_conlat_1) ).
thf(294,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(8,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(126,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)],[8]) ).
thf(12,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(136,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(85,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(427,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)],[85]) ).
thf(31,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(200,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,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(111,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)],[6]) ).
thf(7,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(122,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
? [A: $i] : ( l1_conlat_1 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_conlat_1) ).
thf(222,plain,
? [A: $i] : ( l1_conlat_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(481,plain,
$false,
inference(cvc4,[status(thm)],[169,155,342,139,408,308,247,379,269,385,153,174,185,320,436,344,157,189,416,261,216,238,353,280,453,132,312,206,381,102,349,392,192,165,252,97,285,224,193,256,109,328,457,129,134,266,425,148,180,444,375,402,259,406,274,362,245,318,434,271,455,299,438,431,241,167,150,414,263,177,441,446,143,250,450,203,218,104,383,346,315,183,422,373,305,358,283,294,126,136,427,200,111,122,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT338+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 14:10:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.02 % [INFO] Parsing done (175ms).
% 1.44/1.03 % [INFO] Running in sequential loop mode.
% 1.81/1.22 % [INFO] eprover registered as external prover.
% 1.81/1.22 % [INFO] cvc4 registered as external prover.
% 1.81/1.22 % [INFO] Scanning for conjecture ...
% 2.10/1.30 % [INFO] Found a conjecture and 105 axioms. Running axiom selection ...
% 2.39/1.37 % [INFO] Axiom selection finished. Selected 94 axioms (removed 11 axioms).
% 2.73/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.73/1.47 % [INFO] Type checking passed.
% 2.73/1.47 % [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 ...
% 6.36/2.58 % External prover 'cvc4' found a proof!
% 6.36/2.58 % [INFO] Killing All external provers ...
% 6.36/2.58 % Time passed: 2059ms (effective reasoning time: 1549ms)
% 6.36/2.58 % 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)>
% 6.36/2.58 % Axioms used in derivation (94): dt_m1_conlat_1, existence_l3_conlat_1, fc1_conlat_2, cc2_conlat_1, cc3_lattices, free_g3_lattices, fc5_conlat_1, dt_k10_conlat_1, redefinition_m2_relset_1, rc14_conlat_1, fc2_conlat_1, fc1_xboole_0, existence_l1_lattices, t1_subset, fc1_conlat_1, fc4_subset_1, existence_l3_lattices, fc4_lattice2, rc2_partfun1, cc4_lattices, abstractness_v6_conlat_1, fc2_lattice2, dt_m2_relset_1, d22_lattice3, fc3_lattice2, rc12_conlat_1, fc4_conlat_1, rc11_lattices, dt_l1_lattices, dt_k9_conlat_1, rc3_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, rc9_conlat_1, t5_subset, existence_m1_relset_1, dt_l3_lattices, dt_l2_lattices, t2_tarski, t4_subset, existence_l2_conlat_1, cc1_funct_2, free_g3_conlat_1, t7_boole, rc3_struct_0, fc1_subset_1, fc5_lattice2, rc1_subset_1, rc10_conlat_1, cc1_lattices, rc1_funct_2, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, dt_k16_lattice3, dt_k15_lattice3, d23_conlat_1, existence_m2_relset_1, rc11_conlat_1, existence_l1_conlat_1, dt_g3_conlat_1, dt_u4_conlat_1, fc1_struct_0, cc6_funct_2, t35_conlat_1, reflexivity_r1_tarski, fc3_conlat_1, dt_u5_conlat_1, dt_g3_lattices, rc6_lattices, abstractness_v3_lattices, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_m1_conlat_1, existence_l1_struct_0, rc8_conlat_1, cc5_funct_2, dt_u2_lattices, redefinition_k8_conlat_1, dt_k7_conlat_1, dt_k8_conlat_1, rc2_xboole_0, fraenkel_a_2_1_lattice3, fc3_lattices, dt_k11_conlat_1, dt_l2_conlat_1, rc13_conlat_1, antisymmetry_r2_hidden, cc2_lattices
% 6.36/2.58 % No. of inferences in proof: 192
% 6.36/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2059 ms resp. 1549 ms w/o parsing
% 6.88/2.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.88/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------