%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT305+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:08 AM UTC 2026
% Result : Theorem 15.30s 4.71s
% Output : Refutation 14.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 86
% Syntax : Number of formulae : 219 ( 83 unt; 0 typ; 14 def)
% Number of atoms : 717 ( 74 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2183 ( 195 ~; 40 |; 290 &;1526 @)
% ( 5 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 17 con; 0-6 aty)
% Number of variables : 313 ( 0 ^; 254 !; 45 ?; 313 :)
% ( 0 !>; 0 ?*; 0 @-; 14 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_decl,type,
v10_lattices: $i > $o ).
thf(l3_lattices_decl,type,
l3_lattices: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k18_filter_2_decl,type,
k18_filter_2: $i > $i > $i ).
thf(k4_lattices_decl,type,
k4_lattices: $i > $i > $i > $i ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v1_realset1_decl,type,
v1_realset1: $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(v6_lattices_decl,type,
v6_lattices: $i > $o ).
thf(m2_filter_2_decl,type,
m2_filter_2: $i > $i > $o ).
thf(v7_lattices_decl,type,
v7_lattices: $i > $o ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(a_2_0_filter_2_decl,type,
a_2_0_filter_2: $i > $i > $i ).
thf(v8_lattices_decl,type,
v8_lattices: $i > $o ).
thf(v9_lattices_decl,type,
v9_lattices: $i > $o ).
thf(r3_lattices_decl,type,
r3_lattices: $i > $i > $i > $o ).
thf(r1_lattices_decl,type,
r1_lattices: $i > $i > $i > $o ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(k2_lattices_decl,type,
k2_lattices: $i > $i > $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v4_lattices_decl,type,
v4_lattices: $i > $o ).
thf(v5_lattices_decl,type,
v5_lattices: $i > $o ).
thf(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk22_decl,type,
sk22: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( sk1 @ k18_filter_2 ) @ ( A @ ( B @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
& ( A @ ( sk1 @ k18_filter_2 ) @ ( B @ ( A @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
& ( A @ ( sk1 @ k18_filter_2 ) @ ( A @ r2_hidden ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ ( A @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
& ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( A @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
& ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(23,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(144,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_realset1) ).
thf(123,plain,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(127,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(178,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(21,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(138,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(249,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(115,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
thf(269,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_realset1) ).
thf(119,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(120,plain,
( ( sk7 @ v1_realset1 )
& ~ ( sk7 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[119]) ).
thf(122,plain,
sk7 @ v1_realset1,
inference(cnfConj,[status(thm)],[120]) ).
thf(124,plain,
( ~ ( sk8 @ v1_realset1 )
& ~ ( sk8 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[123]) ).
thf(126,plain,
~ ( sk8 @ v1_realset1 ),
inference(cnfConj,[status(thm)],[124]) ).
thf(338,plain,
( ( ( sk8 @ v1_realset1 )
!= ( sk7 @ v1_realset1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,126]) ).
thf(339,plain,
( ( sk8 @ v1_realset1 )
!= ( sk7 @ v1_realset1 ) ),
inference(simp,[status(thm)],[338]) ).
thf(340,plain,
sk8 != sk7,
inference(simp,[status(thm)],[339]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(151,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(152,plain,
( ( sk12 @ v2_funct_1 )
& ( sk12 @ v1_funct_1 )
& ( sk12 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[151]) ).
thf(153,plain,
sk12 @ v1_relat_1,
inference(cnfConj,[status(thm)],[152]) ).
thf(31,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(173,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(174,plain,
sk15 @ l2_lattices,
inference(cnf,[status(esa)],[173]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(288,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(184,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(125,plain,
~ ( sk8 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[124]) ).
thf(41,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(196,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(156,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(157,plain,
sk13 @ l1_struct_0,
inference(cnf,[status(esa)],[156]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(74,plain,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(75,plain,
( ( ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) )
& ( sk1 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ) )
& ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
& ( sk1 @ l3_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[74]) ).
thf(78,plain,
sk1 @ v10_lattices,
inference(cnfConj,[status(thm)],[75]) ).
thf(60,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(261,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k18_filter_2 ) )
= ( B @ ( A @ a_2_0_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
thf(211,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k18_filter_2 ) )
= ( B @ ( A @ a_2_0_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(106,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(238,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(121,plain,
~ ( sk7 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[120]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(221,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(133,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(265,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(72,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(312,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(116,plain,
( ( sk6 @ v1_funct_1 )
& ( sk6 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
sk6 @ v1_relat_1,
inference(cnfConj,[status(thm)],[116]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(102,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(302,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(192,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(275,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(134,plain,
( ( sk10 @ v1_funct_1 )
& ( sk10 @ v1_xboole_0 )
& ( sk10 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[133]) ).
thf(137,plain,
sk10 @ v1_funct_1,
inference(cnfConj,[status(thm)],[134]) ).
thf(56,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(252,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(10,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(104,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(105,plain,
sk5 @ v1_xboole_0,
inference(cnf,[status(esa)],[104]) ).
thf(327,plain,
( ( ( sk8 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,125]) ).
thf(328,plain,
( ( sk8 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[327]) ).
thf(329,plain,
sk8 != sk5,
inference(simp,[status(thm)],[328]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_2) ).
thf(188,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(141,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(77,plain,
sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(96,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(128,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[127]) ).
thf(129,plain,
~ ( sk9 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[128]) ).
thf(341,plain,
( ( ( sk9 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,129]) ).
thf(342,plain,
( ( sk9 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[341]) ).
thf(343,plain,
sk9 != sk5,
inference(simp,[status(thm)],[342]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(166,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(262,plain,
( ~ ( sk22 @ v3_struct_0 )
& ( sk22 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[261]) ).
thf(264,plain,
~ ( sk22 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[262]) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(180,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(149,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k18_filter_2 ) @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_filter_2) ).
thf(286,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k18_filter_2 ) @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(118,plain,
sk6 @ v1_funct_1,
inference(cnfConj,[status(thm)],[116]) ).
thf(30,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(171,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(172,plain,
sk14 @ l1_lattices,
inference(cnf,[status(esa)],[171]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_realset1) ).
thf(113,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(81,plain,
sk1 @ l3_lattices,
inference(cnfConj,[status(thm)],[75]) ).
thf(50,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(230,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(76,plain,
sk1 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(245,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(79,plain,
( ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(331,plain,
( ~ $true
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
!= ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(eqfactor_ordered,[status(thm)],[79]) ).
thf(335,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) )
!= ( sk2 @ ( sk1 @ k18_filter_2 ) ) )
| ( ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(337,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(344,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 )
| ( sk1 != sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(345,plain,
( ( sk3 != sk2 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[344]) ).
thf(155,plain,
sk12 @ v2_funct_1,
inference(cnfConj,[status(thm)],[152]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(108,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(130,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( C @ ( B @ ( A @ r1_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(223,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r1_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(70,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(306,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(135,plain,
sk10 @ v1_relat_1,
inference(cnfConj,[status(thm)],[134]) ).
thf(80,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(330,plain,
( ~ $true
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
!= ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(eqfactor_ordered,[status(thm)],[79]) ).
thf(333,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) )
!= ( sk2 @ ( sk1 @ k18_filter_2 ) ) )
| ( ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(336,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ k4_lattices ) ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[333]) ).
thf(154,plain,
sk12 @ v1_funct_1,
inference(cnfConj,[status(thm)],[152]) ).
thf(32,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(175,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k2_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(258,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k2_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_realset1) ).
thf(158,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(186,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( B @ ( C @ ( A @ k4_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(235,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( B @ ( C @ ( A @ k4_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(214,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(300,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).
thf(315,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(24,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(146,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(190,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(273,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(324,plain,
( ( ( sk7 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,121]) ).
thf(325,plain,
( ( sk7 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
sk7 != sk5,
inference(simp,[status(thm)],[325]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(136,plain,
sk10 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[134]) ).
thf(355,plain,
( ~ $true
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) @ r2_hidden ) )
!= ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) )
| ( sk3 != sk2 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(eqfactor_ordered,[status(thm)],[345]) ).
thf(357,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) )
!= ( sk2 @ ( sk1 @ k18_filter_2 ) ) )
| ( ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) )
!= sk2 )
| ( sk3 != sk2 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(358,plain,
( ( ( sk3 @ ( sk2 @ ( sk1 @ k4_lattices ) ) )
!= sk2 )
| ( sk3 != sk2 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk2 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(111,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(232,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(100,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(57,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(254,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r3_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(227,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r3_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1413,plain,
$false,
inference(e,[status(thm)],[144,123,127,178,138,249,88,115,308,269,340,153,174,288,184,125,196,157,78,261,211,106,238,121,84,221,133,265,312,74,117,85,102,302,297,192,275,137,252,329,156,188,141,256,77,96,173,129,343,105,205,166,264,180,149,176,286,118,172,113,219,81,230,76,245,345,155,108,130,223,306,135,80,336,154,175,87,203,104,258,158,186,171,119,235,82,214,151,300,315,146,190,273,326,94,126,136,358,79,111,232,100,254,227,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT305+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 20:39:32 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.24 % [INFO] Parsing done (265ms).
% 1.47/1.26 % [INFO] Running in sequential loop mode.
% 2.35/1.66 % [INFO] eprover registered as external prover.
% 2.35/1.67 % [INFO] Scanning for conjecture ...
% 2.56/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 83 axioms. Running axiom selection ...
% 2.95/1.91 % [INFO] Axiom selection finished. Selected 71 axioms (removed 12 axioms).
% 2.95/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 3.26/2.03 % [INFO] Type checking passed.
% 3.26/2.03 % [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 ...
% 15.30/4.70 % External prover 'e' found a proof!
% 15.30/4.70 % [INFO] Killing All external provers ...
% 15.30/4.71 % Time passed: 4171ms (effective reasoning time: 3441ms)
% 15.30/4.71 % 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)>
% 15.30/4.71 % Axioms used in derivation (71): redefinition_m2_relset_1, rc3_funct_1, dt_m2_relset_1, t4_subset, rc2_realset1, redefinition_r3_lattices, redefinition_k2_binop_1, d2_lattices, rc1_realset1, fc1_xboole_0, existence_l1_lattices, d5_tarski, t1_subset, fc4_subset_1, fc3_realset1, existence_l3_lattices, fc4_lattice2, dt_m2_lattice4, dt_k2_binop_1, rc1_funct_1, reflexivity_r3_lattices, dt_l1_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, fc3_subset_1, t5_subset, d9_filter_2, existence_m1_relset_1, dt_m2_filter_2, dt_l3_lattices, fc2_subset_1, dt_l2_lattices, t2_tarski, t7_boole, cc1_funct_1, rc3_struct_0, commutativity_k4_lattices, fc1_subset_1, fc5_lattice2, rc2_funct_1, rc1_subset_1, cc1_lattices, cc2_funct_1, fraenkel_a_2_0_filter_2, t3_subset, cc1_relset_1, dt_u1_lattices, existence_m1_subset_1, commutativity_k2_tarski, existence_m2_relset_1, existence_m2_lattice4, fc1_struct_0, dt_k4_lattices, rc1_lattice4, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, dt_k2_lattices, dt_k18_filter_2, cc1_realset1, d1_binop_1, rc2_xboole_0, existence_m2_filter_2, t23_lattices, antisymmetry_r2_hidden, cc2_lattices, redefinition_k4_lattices
% 15.30/4.71 % No. of inferences in proof: 205
% 15.30/4.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4171 ms resp. 3441 ms w/o parsing
% 14.21/4.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.21/4.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------