TSTP Solution File: LAT289+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT289+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:27:23 EDT 2023
% Result : Theorem 5.80s 2.39s
% Output : Refutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 135
% Syntax : Number of formulae : 216 ( 17 unt; 56 typ; 0 def)
% Number of atoms : 734 ( 15 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 1809 ( 132 ~; 2 |; 382 &;1103 @)
% ( 5 <=>; 185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 56 usr; 2 con; 0-4 aty)
% Number of variables : 285 ( 0 ^; 248 !; 37 ?; 285 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(m1_filter_0_type,type,
m1_filter_0: $i > $i > $o ).
thf(v1_filter_0_type,type,
v1_filter_0: $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k7_lopclset_type,type,
k7_lopclset: $i > $i ).
thf(k9_lopclset_type,type,
k9_lopclset: $i > $i ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(v1_finsub_1_type,type,
v1_finsub_1: $i > $o ).
thf(v3_finsub_1_type,type,
v3_finsub_1: $i > $o ).
thf(v4_finsub_1_type,type,
v4_finsub_1: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k8_lopclset_type,type,
k8_lopclset: $i > $i ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(v1_xcmplx_0_type,type,
v1_xcmplx_0: $i > $o ).
thf(v4_ordinal2_type,type,
v4_ordinal2: $i > $o ).
thf(v1_xreal_0_type,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_type,type,
v1_rat_1: $i > $o ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(a_1_1_lopclset_type,type,
a_1_1_lopclset: $i > $i ).
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(v12_lattices_type,type,
v12_lattices: $i > $o ).
thf(3,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(92,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(129,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(140,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(55,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_membered) ).
thf(263,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
thf(170,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(120,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)],[12]) ).
thf(32,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(185,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)],[32]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(257,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)],[53]) ).
thf(13,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(125,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(196,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(23,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(157,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(152,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
thf(289,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(216,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)],[42]) ).
thf(40,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(211,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(253,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
thf(221,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(17,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).
thf(133,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(116,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(206,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(248,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)],[50]) ).
thf(80,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(380,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(62,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(302,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(349,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)],[74]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(165,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(67,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(317,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(33,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(188,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)],[33]) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(109,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)],[8]) ).
thf(45,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(225,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(339,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(5,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
thf(96,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(72,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(343,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)],[72]) ).
thf(7,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(105,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)],[7]) ).
thf(65,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(311,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)],[65]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(148,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_lopclset) ).
thf(279,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(78,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(375,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(11,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(118,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(204,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)],[37]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(259,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(47,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(236,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(31,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
<=> ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lopclset) ).
thf(181,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
=> ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) )
=> ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(159,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)],[24]) ).
thf(29,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_membered) ).
thf(172,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_lopclset) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(81,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(377,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)],[79]) ).
thf(49,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(245,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(6,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
thf(98,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(57,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(271,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)],[57]) ).
thf(61,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_lopclset) ).
thf(299,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(167,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)],[27]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(255,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(209,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)],[39]) ).
thf(14,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
thf(127,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(75,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k9_lopclset @ A ) )
& ( v1_funct_2 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) )
& ( m2_relset_1 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_lopclset) ).
thf(359,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k9_lopclset @ A ) )
& ( v1_funct_2 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) )
& ( m2_relset_1 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(22,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(154,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(143,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)],[19]) ).
thf(76,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_membered) ).
thf(363,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(77,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(368,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(68,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lopclset) ).
thf(319,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(9,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(114,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(73,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_membered) ).
thf(346,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(214,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)],[41]) ).
thf(59,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_membered) ).
thf(287,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(66,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k7_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lopclset) ).
thf(315,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k7_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(34,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_membered) ).
thf(190,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(63,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_lopclset @ A ) )
& ( v1_funct_1 @ ( k8_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_lopclset) ).
thf(305,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_lopclset @ A ) )
& ( v1_funct_1 @ ( k8_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(48,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_membered) ).
thf(239,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(71,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lopclset) ).
thf(341,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(56,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lopclset @ A )
= ( a_1_1_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lopclset) ).
thf(268,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lopclset @ A )
= ( a_1_1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(94,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) )
=> ( v4_finsub_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(131,plain,
! [A: $i] :
( ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) )
=> ( v4_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [A: $i] :
( ( v4_finsub_1 @ A )
=> ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(178,plain,
! [A: $i] :
( ( v4_finsub_1 @ A )
=> ( ( v1_finsub_1 @ A )
& ( v3_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_membered) ).
thf(200,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
& ( v1_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v3_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(227,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
& ( v1_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v3_finsub_1 @ ( k1_zfmisc_1 @ A ) )
& ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(69,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(337,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(383,plain,
$false,
inference(cvc4,[status(thm)],[92,129,140,263,170,308,120,185,257,125,196,157,152,289,216,211,253,221,133,116,206,248,380,302,349,165,317,188,109,225,339,96,343,105,311,148,279,375,118,204,259,236,181,159,172,219,81,377,245,98,271,299,167,255,209,127,359,154,143,363,368,319,114,346,214,287,315,190,305,239,341,268,94,131,178,163,200,227,337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT289+1 : TPTP v8.1.2. Released v3.4.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 14:18:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.03 % [INFO] Parsing done (161ms).
% 1.46/1.03 % [INFO] Running in sequential loop mode.
% 1.96/1.24 % [INFO] eprover registered as external prover.
% 1.96/1.24 % [INFO] cvc4 registered as external prover.
% 1.96/1.24 % [INFO] Scanning for conjecture ...
% 1.96/1.32 % [INFO] Found a conjecture and 86 axioms. Running axiom selection ...
% 2.43/1.41 % [INFO] Axiom selection finished. Selected 78 axioms (removed 8 axioms).
% 2.70/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.70/1.50 % [INFO] Type checking passed.
% 2.79/1.50 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.80/2.39 % External prover 'cvc4' found a proof!
% 5.80/2.39 % [INFO] Killing All external provers ...
% 5.80/2.39 % Time passed: 1860ms (effective reasoning time: 1351ms)
% 5.80/2.39 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.80/2.39 % Axioms used in derivation (78): redefinition_m2_relset_1, rc1_lopclset, cc2_finsub_1, dt_l1_lattices, t5_subset, cc17_membered, cc12_membered, cc2_finset_1, d5_lopclset, fc1_finsub_1, rc4_finset_1, cc6_lattices, cc10_membered, existence_l1_lattices, t1_subset, dt_k9_lopclset, existence_l3_lattices, rc1_membered, rc2_partfun1, cc4_lattices, dt_m2_relset_1, dt_k8_lopclset, t6_boole, existence_l2_lattices, cc19_membered, existence_m1_relset_1, dt_l3_lattices, dt_k8_funct_2, dt_l2_lattices, fc6_membered, t2_tarski, cc11_membered, cc5_lattices, t4_subset, fraenkel_a_1_1_lopclset, cc1_funct_2, cc20_membered, t7_boole, rc3_struct_0, cc4_membered, cc1_lattices, rc1_funct_2, cc18_membered, existence_m1_filter_0, t3_subset, cc1_relset_1, cc13_membered, existence_m1_subset_1, cc15_membered, redefinition_k9_lopclset, cc3_lattices, dt_k7_lopclset, existence_m2_relset_1, t21_lopclset, cc1_finsub_1, fc1_struct_0, cc6_funct_2, reflexivity_r1_tarski, cc7_lattices, rc3_finset_1, rc1_finset_1, cc1_finset_1, t8_boole, redefinition_k8_funct_2, rc5_struct_0, t2_subset, cc1_membered, dt_m1_filter_0, cc2_membered, cc3_membered, cc14_membered, existence_l1_struct_0, cc5_funct_2, fc14_finset_1, cc16_membered, fc2_lopclset, antisymmetry_r2_hidden, cc2_lattices
% 5.80/2.39 % No. of inferences in proof: 160
% 5.80/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1860 ms resp. 1351 ms w/o parsing
% 5.80/2.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.80/2.47 % [INFO] Killing All external provers ...
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