TSTP Solution File: LAT345+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT345+4 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:28:01 EDT 2023
% Result : Theorem 110.65s 28.17s
% Output : Refutation 110.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 304
% Syntax : Number of formulae : 562 ( 84 unt; 92 typ; 0 def)
% Number of atoms : 2208 ( 305 equ; 0 cnn)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 8400 ( 543 ~; 15 |; 964 &;6125 @)
% ( 50 <=>; 703 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 14 con; 0-4 aty)
% Number of variables : 1006 ( 0 ^; 906 !; 100 ?;1006 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_conlat_1_type,type,
v3_conlat_1: $i > $o ).
thf(v4_conlat_1_type,type,
v4_conlat_1: $i > $o ).
thf(l2_conlat_1_type,type,
l2_conlat_1: $i > $o ).
thf(v6_conlat_1_type,type,
v6_conlat_1: $i > $i > $o ).
thf(v7_conlat_1_type,type,
v7_conlat_1: $i > $i > $o ).
thf(v9_conlat_1_type,type,
v9_conlat_1: $i > $i > $o ).
thf(l3_conlat_1_type,type,
l3_conlat_1: $i > $i > $o ).
thf(k9_conlat_2_type,type,
k9_conlat_2: $i > $i > $i ).
thf(k7_conlat_2_type,type,
k7_conlat_2: $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(k5_finsub_1_type,type,
k5_finsub_1: $i > $i ).
thf(l1_conlat_1_type,type,
l1_conlat_1: $i > $o ).
thf(v1_conlat_1_type,type,
v1_conlat_1: $i > $o ).
thf(u1_conlat_1_type,type,
u1_conlat_1: $i > $i ).
thf(u2_conlat_1_type,type,
u2_conlat_1: $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k2_conlat_1_type,type,
k2_conlat_1: $i > $i ).
thf(k12_mcart_1_type,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(u3_conlat_1_type,type,
u3_conlat_1: $i > $i ).
thf(r1_conlat_1_type,type,
r1_conlat_1: $i > $i > $i > $o ).
thf(r3_lattices_type,type,
r3_lattices: $i > $i > $i > $o ).
thf(k11_conlat_1_type,type,
k11_conlat_1: $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k4_conlat_2_type,type,
k4_conlat_2: $i > $i ).
thf(k5_conlat_2_type,type,
k5_conlat_2: $i > $i ).
thf(k3_conlat_2_type,type,
k3_conlat_2: $i > $i > $i ).
thf(k15_lattice3_type,type,
k15_lattice3: $i > $i > $i ).
thf(k1_pre_topc_type,type,
k1_pre_topc: $i > $i ).
thf(k6_conlat_1_type,type,
k6_conlat_1: $i > $i ).
thf(k2_conlat_2_type,type,
k2_conlat_2: $i > $i > $i ).
thf(k5_conlat_1_type,type,
k5_conlat_1: $i > $i ).
thf(v2_conlat_1_type,type,
v2_conlat_1: $i > $o ).
thf(k1_conlat_1_type,type,
k1_conlat_1: $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(g3_conlat_1_type,type,
g3_conlat_1: $i > $i > $i > $i ).
thf(k16_lattice3_type,type,
k16_lattice3: $i > $i > $i ).
thf(a_2_3_conlat_1_type,type,
a_2_3_conlat_1: $i > $i > $i ).
thf(a_2_2_conlat_1_type,type,
a_2_2_conlat_1: $i > $i > $i ).
thf(a_2_1_conlat_1_type,type,
a_2_1_conlat_1: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k6_relset_1_type,type,
k6_relset_1: $i > $i > $i > $i ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(a_2_0_conlat_1_type,type,
a_2_0_conlat_1: $i > $i > $i ).
thf(m3_conlat_1_type,type,
m3_conlat_1: $i > $i > $i > $o ).
thf(a_2_0_closure1_type,type,
a_2_0_closure1: $i > $i > $i ).
thf(g2_conlat_1_type,type,
g2_conlat_1: $i > $i > $i > $i ).
thf(m1_conlat_1_type,type,
m1_conlat_1: $i > $i > $o ).
thf(m2_conlat_1_type,type,
m2_conlat_1: $i > $i > $i > $o ).
thf(u4_conlat_1_type,type,
u4_conlat_1: $i > $i > $i ).
thf(v8_conlat_1_type,type,
v8_conlat_1: $i > $i > $o ).
thf(u5_conlat_1_type,type,
u5_conlat_1: $i > $i > $i ).
thf(v11_conlat_1_type,type,
v11_conlat_1: $i > $i > $o ).
thf(v10_conlat_1_type,type,
v10_conlat_1: $i > $i > $o ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(k8_conlat_1_type,type,
k8_conlat_1: $i > $i ).
thf(k10_conlat_1_type,type,
k10_conlat_1: $i > $i ).
thf(k9_conlat_1_type,type,
k9_conlat_1: $i > $i ).
thf(k1_zf_colla_type,type,
k1_zf_colla: $i > $i > $i ).
thf(a_1_0_conlat_1_type,type,
a_1_0_conlat_1: $i > $i ).
thf(r2_conlat_1_type,type,
r2_conlat_1: $i > $i > $i > $o ).
thf(k12_conlat_1_type,type,
k12_conlat_1: $i > $i > $i ).
thf(k8_conlat_2_type,type,
k8_conlat_2: $i > $i > $i ).
thf(k4_conlat_1_type,type,
k4_conlat_1: $i > $i ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k7_conlat_1_type,type,
k7_conlat_1: $i > $i ).
thf(a_2_5_conlat_2_type,type,
a_2_5_conlat_2: $i > $i > $i ).
thf(m1_lattice4_type,type,
m1_lattice4: $i > $i > $i > $o ).
thf(k10_conlat_2_type,type,
k10_conlat_2: $i > $i ).
thf(k1_lattice2_type,type,
k1_lattice2: $i > $i ).
thf(a_2_4_conlat_2_type,type,
a_2_4_conlat_2: $i > $i > $i ).
thf(k1_conlat_2_type,type,
k1_conlat_2: $i > $i > $i ).
thf(k3_conlat_1_type,type,
k3_conlat_1: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk24_type,type,
sk24: $i ).
thf(sk29_type,type,
sk29: $i ).
thf(sk32_type,type,
sk32: $i ).
thf(sk48_type,type,
sk48: $i ).
thf(sk53_type,type,
sk53: $i ).
thf(sk58_type,type,
sk58: $i ).
thf(sk69_type,type,
sk69: $i ).
thf(sk71_type,type,
sk71: $i ).
thf(sk76_type,type,
sk76: $i ).
thf(sk77_type,type,
sk77: $i ).
thf(98,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v11_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( B
= ( k6_conlat_1 @ A ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ( B
= ( g3_conlat_1 @ A @ C @ D ) )
& ( C
= ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) )
& ( D
= ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_conlat_1) ).
thf(645,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v11_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( ( B
= ( k6_conlat_1 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ( B
= ( g3_conlat_1 @ A @ C @ D ) )
& ( C
= ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) )
& ( D
= ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ( B
= ( g3_conlat_1 @ A @ C @ D ) )
& ( C
= ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) )
& ( D
= ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) ) )
=> ( B
= ( k6_conlat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(29,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(365,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ( v6_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
& ( v9_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
& ( l3_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_conlat_1) ).
thf(1105,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ( v6_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
& ( v9_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
& ( l3_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(134,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A ) )
<=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_conlat_1) ).
thf(846,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) )
= B ) )
& ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) )
= B )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(100,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
= ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_conlat_1) ).
thf(666,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
= ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(201,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v6_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ~ ( v7_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ( v9_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ( v10_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ( l3_conlat_1 @ ( k5_conlat_1 @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_conlat_1) ).
thf(1110,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v6_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ~ ( v7_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ( v9_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ( v10_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
& ( l3_conlat_1 @ ( k5_conlat_1 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(147,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(909,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(628,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(172,axiom,
? [A: $i] :
( ( l2_conlat_1 @ A )
& ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_conlat_1) ).
thf(1002,plain,
? [A: $i] :
( ( l2_conlat_1 @ A )
& ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1005,plain,
l2_conlat_1 @ sk77,
inference(cnf,[status(esa)],[1002]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k9_conlat_2 @ ( k7_conlat_2 @ A ) @ ( k9_conlat_2 @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_conlat_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k9_conlat_2 @ ( k7_conlat_2 @ A ) @ ( k9_conlat_2 @ A @ B ) )
= B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(214,plain,
~ ! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k9_conlat_2 @ ( k7_conlat_2 @ A ) @ ( k9_conlat_2 @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(217,plain,
l2_conlat_1 @ sk1,
inference(cnf,[status(esa)],[214]) ).
thf(170,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( r2_conlat_1 @ A @ B @ C )
<=> ( r1_tarski @ ( u5_conlat_1 @ A @ C ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_conlat_1) ).
thf(994,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( ( r2_conlat_1 @ A @ B @ C )
=> ( r1_tarski @ ( u5_conlat_1 @ A @ C ) @ ( u5_conlat_1 @ A @ B ) ) )
& ( ( r1_tarski @ ( u5_conlat_1 @ A @ C ) @ ( u5_conlat_1 @ A @ B ) )
=> ( r2_conlat_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(741,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(379,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_conlat_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_conlat_1 @ B ) )
=> ( ( r2_hidden @ E @ C )
=> ( r1_conlat_1 @ B @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_conlat_1) ).
thf(511,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_conlat_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_conlat_1 @ B ) )
=> ( ( r2_hidden @ E @ C )
=> ( r1_conlat_1 @ B @ E @ D ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_conlat_1 @ B ) )
=> ( ( r2_hidden @ E @ C )
=> ( r1_conlat_1 @ B @ E @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_2_0_conlat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(103,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( r1_tarski @ B @ D ) )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_conlat_1) ).
thf(677,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( r1_tarski @ B @ D ) )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(35,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ( k3_conlat_2 @ A @ B )
= ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_conlat_2) ).
thf(384,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ( k3_conlat_2 @ A @ B )
= ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(210,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_conlat_1) ).
thf(1137,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(550,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(500,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) )
<=> ( r2_hidden @ B @ ( k1_zf_colla @ A @ k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zf_colla) ).
thf(797,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) )
=> ( r2_hidden @ B @ ( k1_zf_colla @ A @ k1_xboole_0 ) ) )
& ( ( r2_hidden @ B @ ( k1_zf_colla @ A @ k1_xboole_0 ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(107,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(698,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(189,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
= ( k5_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_conlat_1) ).
thf(1063,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
= ( k5_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(153,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ ( k7_conlat_2 @ A ) )
& ( l3_conlat_1 @ C @ ( k7_conlat_2 @ A ) ) )
=> ( ( C
= ( k8_conlat_2 @ A @ B ) )
<=> ( ( ( u4_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
= ( u5_conlat_1 @ A @ B ) )
& ( ( u5_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
= ( u4_conlat_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_conlat_2) ).
thf(930,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ ( k7_conlat_2 @ A ) )
& ( l3_conlat_1 @ C @ ( k7_conlat_2 @ A ) ) )
=> ( ( ( C
= ( k8_conlat_2 @ A @ B ) )
=> ( ( ( u4_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
= ( u5_conlat_1 @ A @ B ) )
& ( ( u5_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
= ( u4_conlat_1 @ A @ B ) ) ) )
& ( ( ( ( u4_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
= ( u5_conlat_1 @ A @ B ) )
& ( ( u5_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
= ( u4_conlat_1 @ A @ B ) ) )
=> ( C
= ( k8_conlat_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(40,axiom,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A )
& ~ ( v2_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_conlat_1) ).
thf(402,plain,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A )
& ~ ( v2_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(404,plain,
v1_conlat_1 @ sk29,
inference(cnf,[status(esa)],[402]) ).
thf(123,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_conlat_1) ).
thf(782,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lopclset) ).
thf(417,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(565,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(109,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v10_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( B
= ( k5_conlat_1 @ A ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ( B
= ( g3_conlat_1 @ A @ C @ D ) )
& ( C
= ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) )
& ( D
= ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_conlat_1) ).
thf(702,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v10_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( ( B
= ( k5_conlat_1 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ( B
= ( g3_conlat_1 @ A @ C @ D ) )
& ( C
= ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) )
& ( D
= ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ( B
= ( g3_conlat_1 @ A @ C @ D ) )
& ( C
= ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) )
& ( D
= ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) )
=> ( B
= ( k5_conlat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(26,axiom,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_conlat_1) ).
thf(356,plain,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(357,plain,
v1_conlat_1 @ sk24,
inference(cnf,[status(esa)],[356]) ).
thf(96,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_conlat_1) ).
thf(638,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(195,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v8_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ~ ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A )
& ( B
!= ( k5_conlat_1 @ A ) )
& ( B
!= ( k6_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_conlat_1) ).
thf(1087,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v8_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ~ ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A )
& ( B
!= ( k5_conlat_1 @ A ) )
& ( B
!= ( k6_conlat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(163,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( r2_conlat_1 @ A @ C @ B )
<=> ( r1_tarski @ ( u5_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_conlat_1) ).
thf(969,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( ( r2_conlat_1 @ A @ C @ B )
=> ( r1_tarski @ ( u5_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ C ) ) )
& ( ( r1_tarski @ ( u5_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ C ) )
=> ( r2_conlat_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(228,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(261,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
& ( v9_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
& ( l3_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_conlat_2) ).
thf(817,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
& ( v9_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
& ( l3_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(145,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(902,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(175,axiom,
! [A: $i] :
( ( ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( v8_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_conlat_1) ).
thf(1013,plain,
! [A: $i] :
( ( ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( v8_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(770,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(216,plain,
v9_conlat_1 @ sk2 @ sk1,
inference(cnf,[status(esa)],[214]) ).
thf(151,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
=> ( ( k12_conlat_1 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d24_conlat_1) ).
thf(924,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
=> ( ( k12_conlat_1 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(125,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(789,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(81,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(591,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(183,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_conlat_1) ).
thf(1040,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(97,axiom,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A )
& ( v2_conlat_1 @ A )
& ( v3_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_conlat_1) ).
thf(640,plain,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A )
& ( v2_conlat_1 @ A )
& ( v3_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(641,plain,
v3_conlat_1 @ sk48,
inference(cnf,[status(esa)],[640]) ).
thf(220,plain,
~ ( v3_conlat_1 @ sk1 ),
inference(cnf,[status(esa)],[214]) ).
thf(1149,plain,
( ( v3_conlat_1 @ sk48 )
!= ( v3_conlat_1 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[641,220]) ).
thf(1151,plain,
sk48 != sk1,
inference(simp,[status(thm)],[1149]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( r2_hidden @ B @ A ) )
& ( ( r2_hidden @ B @ A )
=> ( m1_subset_1 @ B @ A ) ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( v1_xboole_0 @ B ) )
& ( ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(130,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(821,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_conlat_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u2_conlat_1 @ B ) )
=> ( ( r2_hidden @ E @ C )
=> ( r1_conlat_1 @ B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_conlat_1) ).
thf(480,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_conlat_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u2_conlat_1 @ B ) )
=> ( ( r2_hidden @ E @ C )
=> ( r1_conlat_1 @ B @ D @ E ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
& ( A = D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u2_conlat_1 @ B ) )
=> ( ( r2_hidden @ E @ C )
=> ( r1_conlat_1 @ B @ D @ E ) ) ) )
=> ( r2_hidden @ A @ ( a_2_1_conlat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(353,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ( l3_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_conlat_2) ).
thf(966,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ( l3_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(85,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(602,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_triang_1) ).
thf(397,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(140,axiom,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_gate_1) ).
thf(877,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(159,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ! [D: $i] :
( ( ( v6_conlat_1 @ D @ A )
& ~ ( v7_conlat_1 @ D @ A )
& ( v9_conlat_1 @ D @ A )
& ( l3_conlat_1 @ D @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ D ) )
= ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_conlat_1) ).
thf(956,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ! [D: $i] :
( ( ( v6_conlat_1 @ D @ A )
& ~ ( v7_conlat_1 @ D @ A )
& ( v9_conlat_1 @ D @ A )
& ( l3_conlat_1 @ D @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ D ) )
= ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(191,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_4_conlat_2 @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_conlat_2) ).
thf(1072,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_4_conlat_2 @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(203,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_conlat_1) ).
thf(1119,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
=> ( ( r1_conlat_1 @ A @ B @ C )
<=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u3_conlat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_conlat_1) ).
thf(411,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
=> ( ( ( r1_conlat_1 @ A @ B @ C )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u3_conlat_1 @ A ) ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u3_conlat_1 @ A ) )
=> ( r1_conlat_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(312,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(112,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
=> ( ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
& ( v9_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
& ( l3_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_conlat_2) ).
thf(734,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
=> ( ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
& ( v9_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
& ( l3_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(221,plain,
~ ( v7_conlat_1 @ sk2 @ sk1 ),
inference(cnf,[status(esa)],[214]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(292,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(233,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(155,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v11_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc16_conlat_1) ).
thf(942,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v11_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ! [C: $i] :
( ( m3_conlat_1 @ C @ A @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_conlat_1) ).
thf(761,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ! [C: $i] :
( ( m3_conlat_1 @ C @ A @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(187,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_conlat_1) ).
thf(1057,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(196,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_conlat_1) ).
thf(1091,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(37,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( ( k3_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
= ( k5_conlat_1 @ A ) )
& ( ( k2_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
= ( k6_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_conlat_2) ).
thf(392,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( ( k3_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
= ( k5_conlat_1 @ A ) )
& ( ( k2_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
= ( k6_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,axiom,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A )
& ~ ( v3_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_conlat_1) ).
thf(423,plain,
? [A: $i] :
( ( l1_conlat_1 @ A )
& ( v1_conlat_1 @ A )
& ~ ( v3_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(424,plain,
~ ( v3_conlat_1 @ sk32 ),
inference(cnf,[status(esa)],[423]) ).
thf(93,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_conlat_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_conlat_1) ).
thf(630,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_conlat_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(275,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(91,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_conlat_1) ).
thf(625,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(878,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(polarity_switch,[status(thm)],[877]) ).
thf(879,plain,
~ ( v1_xboole_0 @ sk69 ),
inference(cnf,[status(esa)],[878]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_conlat_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_conlat_1) ).
thf(583,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( m2_conlat_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_conlat_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(179,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] : ( m1_conlat_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_conlat_1) ).
thf(1027,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] : ( m1_conlat_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(104,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( v7_conlat_1 @ B @ A )
<=> ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
& ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_conlat_1) ).
thf(682,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( ( v7_conlat_1 @ B @ A )
=> ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
& ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) )
& ( ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
& ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) )
=> ( v7_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(3,axiom,
! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_measure1) ).
thf(224,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(156,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k4_conlat_1 @ A )
= ( k2_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_conlat_1) ).
thf(948,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k4_conlat_1 @ A )
= ( k2_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(173,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_conlat_1) ).
thf(1006,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u4_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u4_conlat_1) ).
thf(593,plain,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u4_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(137,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 )
= ( u2_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_conlat_1) ).
thf(869,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 )
= ( u2_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(420,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(857,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(139,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
=> ( ( r3_lattices @ ( k11_conlat_1 @ A ) @ B @ C )
<=> ( r2_conlat_1 @ A @ ( k12_conlat_1 @ A @ B ) @ ( k12_conlat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_conlat_1) ).
thf(874,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
=> ( ( ( r3_lattices @ ( k11_conlat_1 @ A ) @ B @ C )
=> ( r2_conlat_1 @ A @ ( k12_conlat_1 @ A @ B ) @ ( k12_conlat_1 @ A @ C ) ) )
& ( ( r2_conlat_1 @ A @ ( k12_conlat_1 @ A @ B ) @ ( k12_conlat_1 @ A @ C ) )
=> ( r3_lattices @ ( k11_conlat_1 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( v4_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) )
& ( l2_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_conlat_1) ).
thf(1143,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( v4_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) )
& ( l2_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(167,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc14_conlat_1) ).
thf(980,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(403,plain,
~ ( v2_conlat_1 @ sk29 ),
inference(cnf,[status(esa)],[402]) ).
thf(52,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ( k2_conlat_2 @ A @ B )
= ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_conlat_2) ).
thf(471,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ( k2_conlat_2 @ A @ B )
= ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(225,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[224]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( a_2_0_closure1 @ A @ C ) @ ( a_2_0_closure1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_closure1) ).
thf(554,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( a_2_0_closure1 @ A @ C ) @ ( a_2_0_closure1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ B @ A )
=> ( B
= ( g3_conlat_1 @ A @ ( u4_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v6_conlat_1) ).
thf(669,plain,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ B @ A )
=> ( B
= ( g3_conlat_1 @ A @ ( u4_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(642,plain,
v2_conlat_1 @ sk48,
inference(cnf,[status(esa)],[640]) ).
thf(105,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ( ( v3_conlat_1 @ A )
<=> ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
| ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_conlat_1) ).
thf(686,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ( ( ( v3_conlat_1 @ A )
=> ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
| ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) )
& ( ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
| ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) )
=> ( v3_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(192,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v10_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc15_conlat_1) ).
thf(1075,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( v10_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(171,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( v10_conlat_1 @ B @ A )
<=> ( ( u4_conlat_1 @ A @ B )
= ( u1_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_conlat_1) ).
thf(997,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( ( v10_conlat_1 @ B @ A )
=> ( ( u4_conlat_1 @ A @ B )
= ( u1_conlat_1 @ A ) ) )
& ( ( ( u4_conlat_1 @ A @ B )
= ( u1_conlat_1 @ A ) )
=> ( v10_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(108,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(700,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(701,plain,
v1_xboole_0 @ sk53,
inference(cnf,[status(esa)],[700]) ).
thf(208,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k3_conlat_1 @ A )
= ( k1_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_conlat_1) ).
thf(1131,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k3_conlat_1 @ A )
= ( k1_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(188,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
= ( k6_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_conlat_1) ).
thf(1060,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
= ( k6_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(911,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(721,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)],[110]) ).
thf(198,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( r2_conlat_1 @ A @ B @ ( k5_conlat_1 @ A ) )
& ( r2_conlat_1 @ A @ ( k6_conlat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_conlat_1) ).
thf(1099,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( r2_conlat_1 @ A @ B @ ( k5_conlat_1 @ A ) )
& ( r2_conlat_1 @ A @ ( k6_conlat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(168,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( v11_conlat_1 @ B @ A )
<=> ( ( u5_conlat_1 @ A @ B )
= ( u2_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_conlat_1) ).
thf(985,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( ( v11_conlat_1 @ B @ A )
=> ( ( u5_conlat_1 @ A @ B )
= ( u2_conlat_1 @ A ) ) )
& ( ( ( u5_conlat_1 @ A @ B )
= ( u2_conlat_1 @ A ) )
=> ( v11_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(59,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
<=> ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_conlat_1) ).
thf(503,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
=> ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) )
& ( ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) )
=> ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(605,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ( ( v6_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_conlat_1) ).
thf(508,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ( ( v6_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(150,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(921,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(118,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_conlat_1) ).
thf(765,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(558,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(121,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( v9_conlat_1 @ B @ A )
<=> ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
= ( u5_conlat_1 @ A @ B ) )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
= ( u4_conlat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_conlat_1) ).
thf(773,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( ( v9_conlat_1 @ B @ A )
=> ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
= ( u5_conlat_1 @ A @ B ) )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
= ( u4_conlat_1 @ A @ B ) ) ) )
& ( ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
= ( u5_conlat_1 @ A @ B ) )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
= ( u4_conlat_1 @ A @ B ) ) )
=> ( v9_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(143,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(888,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(146,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ~ ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
= ( u5_conlat_1 @ A @ B ) )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
= ( u4_conlat_1 @ A @ B ) )
& ( v7_conlat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_conlat_2) ).
thf(906,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ~ ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
= ( u5_conlat_1 @ A @ B ) )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
= ( u4_conlat_1 @ A @ B ) )
& ( v7_conlat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(425,plain,
v1_conlat_1 @ sk32,
inference(cnf,[status(esa)],[423]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_2_0_closure1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure1) ).
thf(745,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_2_0_closure1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r1_tarski @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r1_tarski @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_closure1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(444,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(213,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v8_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ~ ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A )
& ~ ( v10_conlat_1 @ B @ A )
& ~ ( v11_conlat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_conlat_1) ).
thf(1146,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v8_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ~ ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A )
& ~ ( v10_conlat_1 @ B @ A )
& ~ ( v11_conlat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(430,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1153,plain,
( ( v2_conlat_1 @ sk48 )
!= ( v2_conlat_1 @ sk29 ) ),
inference(paramod_ordered,[status(thm)],[642,403]) ).
thf(1154,plain,
sk48 != sk29,
inference(simp,[status(thm)],[1153]) ).
thf(114,axiom,
? [A: $i] : ( l1_conlat_1 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_conlat_1) ).
thf(743,plain,
? [A: $i] : ( l1_conlat_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(822,plain,
( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(miniscope,[status(thm)],[821]) ).
thf(823,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[822]) ).
thf(825,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[823]) ).
thf(826,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[825]) ).
thf(205,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] : ( l3_conlat_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_conlat_1) ).
thf(1124,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] : ( l3_conlat_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(74,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k7_conlat_2 @ A )
= ( g2_conlat_1 @ ( u2_conlat_1 @ A ) @ ( u1_conlat_1 @ A ) @ ( k6_relset_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_conlat_2) ).
thf(562,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k7_conlat_2 @ A )
= ( g2_conlat_1 @ ( u2_conlat_1 @ A ) @ ( u1_conlat_1 @ A ) @ ( k6_relset_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(165,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_5_conlat_2 @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_conlat_2) ).
thf(975,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_5_conlat_2 @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(350,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(102,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( ( u4_conlat_1 @ A @ ( k5_conlat_1 @ A ) )
= ( u1_conlat_1 @ A ) )
& ( ( u5_conlat_1 @ A @ ( k6_conlat_1 @ A ) )
= ( u2_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_conlat_1) ).
thf(672,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( ( u4_conlat_1 @ A @ ( k5_conlat_1 @ A ) )
= ( u1_conlat_1 @ A ) )
& ( ( u5_conlat_1 @ A @ ( k6_conlat_1 @ A ) )
= ( u2_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(611,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)],[88]) ).
thf(124,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_conlat_1) ).
thf(787,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(406,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)],[41]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
& ( v9_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
& ( l3_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_conlat_2) ).
thf(831,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
& ( v9_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
& ( l3_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(219,plain,
v6_conlat_1 @ sk2 @ sk1,
inference(cnf,[status(esa)],[214]) ).
thf(141,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_conlat_2) ).
thf(880,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
=> ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
& ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k1_conlat_2 @ A @ B ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_conlat_2) ).
thf(1122,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k1_conlat_2 @ A @ B ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(84,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(599,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k5_finsub_1 @ A ) )
& ( r1_tarski @ C @ B ) )
=> ( r2_hidden @ C @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_8) ).
thf(377,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k5_finsub_1 @ A ) )
& ( r1_tarski @ C @ B ) )
=> ( r2_hidden @ C @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(169,axiom,
? [A: $i] :
( ( l2_conlat_1 @ A )
& ~ ( v2_conlat_1 @ A )
& ( v4_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_conlat_1) ).
thf(990,plain,
? [A: $i] :
( ( l2_conlat_1 @ A )
& ~ ( v2_conlat_1 @ A )
& ( v4_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(28,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
=> ( ( r1_conlat_1 @ A @ B @ C )
<=> ( r3_lattices @ ( k11_conlat_1 @ A ) @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_conlat_2) ).
thf(362,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
=> ( ( ( r1_conlat_1 @ A @ B @ C )
=> ( r3_lattices @ ( k11_conlat_1 @ A ) @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) ) )
& ( ( r3_lattices @ ( k11_conlat_1 @ A ) @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) )
=> ( r1_conlat_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(76,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ( ( v2_conlat_1 @ A )
<=> ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
& ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_conlat_1) ).
thf(567,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ( ( ( v2_conlat_1 @ A )
=> ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
& ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) )
& ( ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
& ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) )
=> ( v2_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(54,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_tarski @ B ) )
= ( a_2_2_conlat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_conlat_1) ).
thf(477,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_tarski @ B ) )
= ( a_2_2_conlat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(36,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( ( k3_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
= ( k6_conlat_1 @ A ) )
& ( ( k2_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
= ( k5_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_conlat_2) ).
thf(387,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( ( k3_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
= ( k6_conlat_1 @ A ) )
& ( ( k2_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
= ( k5_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k6_relset_1) ).
thf(494,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(19,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(323,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ~ ( v7_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ( v9_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ( l3_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_conlat_2) ).
thf(1029,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( v6_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ~ ( v7_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ( v9_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
& ( l3_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(23,axiom,
! [A: $i] :
~ ( ( A
= ( k1_tarski @ k1_xboole_0 ) )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_gate_1) ).
thf(345,plain,
! [A: $i] :
~ ( ( A
= ( k1_tarski @ k1_xboole_0 ) )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ? [C: $i] : ( m3_conlat_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_conlat_1) ).
thf(552,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ? [C: $i] : ( m3_conlat_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_conlat_1 @ C @ A @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_conlat_1) ).
thf(959,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_conlat_1 @ C @ A @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(184,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( ( ( u4_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( B
= ( k6_conlat_1 @ A ) ) )
& ( ( ( u5_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( B
= ( k5_conlat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_conlat_1) ).
thf(1044,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( ( ( u4_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( B
= ( k6_conlat_1 @ A ) ) )
& ( ( ( u5_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( B
= ( k5_conlat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(190,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( m1_conlat_1 @ B @ A )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_conlat_1) ).
thf(1066,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( m1_conlat_1 @ B @ A )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) ) )
=> ( m1_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(122,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_conlat_1) ).
thf(780,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(176,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k8_conlat_1 @ A ) )
<=> ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_conlat_1) ).
thf(1015,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ ( k8_conlat_1 @ A ) )
=> ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) ) )
& ( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( r2_hidden @ B @ ( k8_conlat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(4,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(226,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(199,axiom,
? [A: $i] :
( ( l2_conlat_1 @ A )
& ( v4_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_conlat_1) ).
thf(1102,plain,
? [A: $i] :
( ( l2_conlat_1 @ A )
& ( v4_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(222,plain,
( ( k9_conlat_2 @ ( k7_conlat_2 @ sk1 ) @ ( k9_conlat_2 @ sk1 @ sk2 ) )
!= sk2 ),
inference(cnf,[status(esa)],[214]) ).
thf(223,plain,
( ( k9_conlat_2 @ ( k7_conlat_2 @ sk1 ) @ ( k9_conlat_2 @ sk1 @ sk2 ) )
!= sk2 ),
inference(lifteq,[status(thm)],[222]) ).
thf(87,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_conlat_1) ).
thf(608,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(181,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_conlat_1 @ ( k7_conlat_2 @ A ) )
& ( v4_conlat_1 @ ( k7_conlat_2 @ A ) )
& ( l2_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_conlat_2) ).
thf(1034,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ~ ( v3_conlat_1 @ ( k7_conlat_2 @ A ) )
& ( v4_conlat_1 @ ( k7_conlat_2 @ A ) )
& ( l2_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(426,plain,
l1_conlat_1 @ sk32,
inference(cnf,[status(esa)],[423]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(548,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)],[67]) ).
thf(152,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_conlat_1) ).
thf(927,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(209,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ! [D: $i] :
( ( ( v6_conlat_1 @ D @ A )
& ~ ( v7_conlat_1 @ D @ A )
& ( v9_conlat_1 @ D @ A )
& ( l3_conlat_1 @ D @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ D ) )
= ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_conlat_1) ).
thf(1134,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ! [D: $i] :
( ( ( v6_conlat_1 @ D @ A )
& ~ ( v7_conlat_1 @ D @ A )
& ( v9_conlat_1 @ D @ A )
& ( l3_conlat_1 @ D @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ D ) )
= ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(193,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ( v8_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_conlat_1) ).
thf(1081,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ? [B: $i] :
( ( l3_conlat_1 @ B @ A )
& ( v6_conlat_1 @ B @ A )
& ( v8_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( u1_conlat_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_conlat_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
& ( A = D )
& ( r1_conlat_1 @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_conlat_1) ).
thf(617,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( u1_conlat_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_conlat_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
& ( A = D )
& ( r1_conlat_1 @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
& ( A = D )
& ( r1_conlat_1 @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_2_conlat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(154,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( r2_conlat_1 @ A @ B @ C )
<=> ( r1_tarski @ ( u4_conlat_1 @ A @ B ) @ ( u4_conlat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_conlat_1) ).
thf(939,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( ( r2_conlat_1 @ A @ B @ C )
=> ( r1_tarski @ ( u4_conlat_1 @ A @ B ) @ ( u4_conlat_1 @ A @ C ) ) )
& ( ( r1_tarski @ ( u4_conlat_1 @ A @ B ) @ ( u4_conlat_1 @ A @ C ) )
=> ( r2_conlat_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(342,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(754,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) )
=> ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(185,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C )
= ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_conlat_1) ).
thf(1049,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C )
= ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(525,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1003,plain,
v4_conlat_1 @ sk77,
inference(cnf,[status(esa)],[1002]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( u2_conlat_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_3_conlat_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
& ( A = D )
& ( r1_conlat_1 @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_conlat_1) ).
thf(690,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B )
& ( m1_subset_1 @ C @ ( u2_conlat_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_conlat_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
& ( A = D )
& ( r1_conlat_1 @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
& ( A = D )
& ( r1_conlat_1 @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_3_conlat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(178,axiom,
? [A: $i] : ( l2_conlat_1 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_conlat_1) ).
thf(1025,plain,
? [A: $i] : ( l2_conlat_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u5_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u5_conlat_1) ).
thf(872,plain,
! [A: $i,B: $i] :
( ( ( l1_conlat_1 @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( m1_subset_1 @ ( u5_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(14,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( k1_tarski @ B )
!= A )
& ! [C: $i,D: $i] :
~ ( ( C != D )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_collsp) ).
thf(282,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( k1_tarski @ B )
!= A )
& ! [C: $i,D: $i] :
~ ( ( C != D )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(142,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(887,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(43,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
= ( k1_funct_1 @ ( k2_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_conlat_2) ).
thf(414,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
= ( k1_funct_1 @ ( k2_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(158,axiom,
! [A: $i] :
( ( ( v2_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( v7_conlat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_conlat_1) ).
thf(954,plain,
! [A: $i] :
( ( ( v2_conlat_1 @ A )
& ( l1_conlat_1 @ A ) )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( v7_conlat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(263,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(993,plain,
l2_conlat_1 @ sk76,
inference(cnf,[status(esa)],[990]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( C = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_hahnban) ).
thf(331,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(441,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)],[49]) ).
thf(194,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_conlat_1) ).
thf(1085,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(157,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k7_conlat_2 @ ( k7_conlat_2 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_conlat_2) ).
thf(951,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( v4_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k7_conlat_2 @ ( k7_conlat_2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(27,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
<=> ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_conlat_1) ).
thf(359,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
=> ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) )
& ( ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) )
=> ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(643,plain,
v1_conlat_1 @ sk48,
inference(cnf,[status(esa)],[640]) ).
thf(182,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( m1_lattice4 @ ( k10_conlat_2 @ A ) @ ( k1_lattice2 @ ( k11_conlat_1 @ A ) ) @ ( k11_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_conlat_2) ).
thf(1038,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( m1_lattice4 @ ( k10_conlat_2 @ A ) @ ( k1_lattice2 @ ( k11_conlat_1 @ A ) ) @ ( k11_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(744,plain,
l1_conlat_1 @ sk58,
inference(cnf,[status(esa)],[743]) ).
thf(177,axiom,
! [A: $i] :
( ( l2_conlat_1 @ A )
=> ( l1_conlat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_conlat_1) ).
thf(1023,plain,
! [A: $i] :
( ( l2_conlat_1 @ A )
=> ( l1_conlat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(89,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(613,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(186,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( ( ( u4_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( v11_conlat_1 @ B @ A ) )
& ( ( ( u5_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( v10_conlat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_conlat_1) ).
thf(1052,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( ( ( u4_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( v11_conlat_1 @ B @ A ) )
& ( ( ( u5_conlat_1 @ A @ B )
= k1_xboole_0 )
=> ( v10_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(864,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(77,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
<=> ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_conlat_1) ).
thf(571,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
=> ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) )
& ( ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
=> ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(83,axiom,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( v8_conlat_1 @ B @ A )
<=> ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
| ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_conlat_1) ).
thf(595,plain,
! [A: $i] :
( ( l1_conlat_1 @ A )
=> ! [B: $i] :
( ( l3_conlat_1 @ B @ A )
=> ( ( ( v8_conlat_1 @ B @ A )
=> ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
| ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) )
& ( ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
| ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) )
=> ( v8_conlat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(497,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(991,plain,
v4_conlat_1 @ sk76,
inference(cnf,[status(esa)],[990]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_conlat_1 @ B @ A ) )
=> ? [C: $i] : ( m2_conlat_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_conlat_1) ).
thf(978,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ( m1_conlat_1 @ B @ A ) )
=> ? [C: $i] : ( m2_conlat_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(211,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C )
= ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_conlat_1) ).
thf(1140,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C )
= ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(6,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(231,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(556,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(539,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(891,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(174,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k8_conlat_1 @ A )
= ( k7_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_conlat_1) ).
thf(1010,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k8_conlat_1 @ A )
= ( k7_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(30,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(368,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(218,plain,
l3_conlat_1 @ sk2 @ sk1,
inference(cnf,[status(esa)],[214]) ).
thf(206,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_conlat_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_conlat_2) ).
thf(1126,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k1_conlat_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(80,axiom,
! [A: $i] :
( ( l2_conlat_1 @ A )
=> ( ( v4_conlat_1 @ A )
=> ( A
= ( g2_conlat_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v4_conlat_1) ).
thf(588,plain,
! [A: $i] :
( ( l2_conlat_1 @ A )
=> ( ( v4_conlat_1 @ A )
=> ( A
= ( g2_conlat_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(161,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k7_conlat_1 @ A )
= ( a_1_0_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_conlat_1) ).
thf(963,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k7_conlat_1 @ A )
= ( a_1_0_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(9,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(258,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(94,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 )
= ( u1_conlat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_conlat_1) ).
thf(632,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 )
= ( u1_conlat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(111,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k11_conlat_1 @ A )
= ( g3_lattices @ ( k8_conlat_1 @ A ) @ ( k10_conlat_1 @ A ) @ ( k9_conlat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d23_conlat_1) ).
thf(731,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( k11_conlat_1 @ A )
= ( g3_lattices @ ( k8_conlat_1 @ A ) @ ( k10_conlat_1 @ A ) @ ( k9_conlat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(64,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(536,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(15,axiom,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(290,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g2_conlat_1 @ A @ B @ C )
= ( g2_conlat_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_conlat_1) ).
thf(914,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g2_conlat_1 @ A @ B @ C )
= ( g2_conlat_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k9_conlat_2 @ A @ B )
= ( k8_conlat_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_conlat_2) ).
thf(1116,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ( ( k9_conlat_2 @ A @ B )
= ( k8_conlat_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(315,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(133,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) )
<=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_conlat_1) ).
thf(835,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
= B ) )
& ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
= B )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( v9_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
& ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(405,plain,
l1_conlat_1 @ sk29,
inference(cnf,[status(esa)],[402]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(273,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(239,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(127,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_conlat_1) ).
thf(801,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(60,axiom,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(506,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(358,plain,
l1_conlat_1 @ sk24,
inference(cnf,[status(esa)],[356]) ).
thf(99,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_conlat_1) ).
thf(664,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( m1_subset_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(400,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( m1_subset_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(131,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
= ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_conlat_1) ).
thf(828,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
= ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(53,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u2_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_tarski @ B ) )
= ( a_2_3_conlat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_conlat_1) ).
thf(474,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u2_conlat_1 @ A ) )
=> ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_tarski @ B ) )
= ( a_2_3_conlat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(119,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(767,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(197,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v6_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ~ ( v7_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ( v9_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ( v11_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ( l3_conlat_1 @ ( k6_conlat_1 @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_conlat_1) ).
thf(1093,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( ( v6_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ~ ( v7_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ( v9_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ( v11_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
& ( l3_conlat_1 @ ( k6_conlat_1 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_conlat_1 @ A @ B @ C )
= ( g3_conlat_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_conlat_1) ).
thf(464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_conlat_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_conlat_1 @ A @ B @ C )
= ( g3_conlat_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(207,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_conlat_1) ).
thf(1129,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(644,plain,
l1_conlat_1 @ sk48,
inference(cnf,[status(esa)],[640]) ).
thf(992,plain,
~ ( v2_conlat_1 @ sk76 ),
inference(cnf,[status(esa)],[990]) ).
thf(1004,plain,
~ ( v3_conlat_1 @ sk77 ),
inference(cnf,[status(esa)],[1002]) ).
thf(1150,plain,
( ( v3_conlat_1 @ sk48 )
!= ( v3_conlat_1 @ sk32 ) ),
inference(paramod_ordered,[status(thm)],[641,424]) ).
thf(1152,plain,
sk48 != sk32,
inference(simp,[status(thm)],[1150]) ).
thf(47,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
= ( k1_funct_1 @ ( k1_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_conlat_2) ).
thf(427,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
= ( k1_funct_1 @ ( k1_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_conlat_1 @ B ) )
<=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) )
& ( A
= ( g3_conlat_1 @ B @ C @ D ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ B @ C @ D ) @ B )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_conlat_1 @ B ) @ C )
= D )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k2_conlat_1 @ B ) @ D )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_conlat_1) ).
thf(803,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ B )
& ( l2_conlat_1 @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_conlat_1 @ B ) )
=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) )
& ( A
= ( g3_conlat_1 @ B @ C @ D ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ B @ C @ D ) @ B )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_conlat_1 @ B ) @ C )
= D )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k2_conlat_1 @ B ) @ D )
= C ) ) )
& ( ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) )
& ( A
= ( g3_conlat_1 @ B @ C @ D ) )
& ~ ( v7_conlat_1 @ ( g3_conlat_1 @ B @ C @ D ) @ B )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_conlat_1 @ B ) @ C )
= D )
& ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k2_conlat_1 @ B ) @ D )
= C ) )
=> ( r2_hidden @ A @ ( a_1_0_conlat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(337,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(922,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[921]) ).
thf(923,plain,
~ ( v1_xboole_0 @ sk71 ),
inference(cnf,[status(esa)],[922]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ! [C: $i] :
( ( m3_conlat_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m3_conlat_1) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
=> ! [C: $i] :
( ( ( m3_conlat_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m3_conlat_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(215,plain,
v4_conlat_1 @ sk1,
inference(cnf,[status(esa)],[214]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(560,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(164,axiom,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ C )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_conlat_1) ).
thf(972,plain,
! [A: $i] :
( ( ~ ( v3_conlat_1 @ A )
& ( l2_conlat_1 @ A ) )
=> ! [B: $i] :
( ( ( v6_conlat_1 @ B @ A )
& ~ ( v7_conlat_1 @ B @ A )
& ( v9_conlat_1 @ B @ A )
& ( l3_conlat_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v6_conlat_1 @ C @ A )
& ~ ( v7_conlat_1 @ C @ A )
& ( v9_conlat_1 @ C @ A )
& ( l3_conlat_1 @ C @ A ) )
=> ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ C )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(74185,plain,
$false,
inference(cvc4,[status(thm)],[645,365,1105,846,666,1110,909,628,1005,217,994,741,379,511,677,384,1137,550,500,797,698,1063,930,404,782,417,565,702,357,638,1087,969,228,261,817,902,1013,770,216,924,789,591,1040,1151,574,821,480,353,966,602,397,877,956,1072,1119,411,312,734,221,292,233,942,761,220,1057,1091,392,424,630,275,625,879,583,1027,682,224,948,1006,356,593,869,420,857,874,1143,980,403,471,225,554,669,642,686,1075,997,701,1131,1060,911,721,1002,1099,985,503,605,508,921,765,558,773,888,906,425,745,444,375,1146,430,1154,423,402,743,826,1124,562,975,641,350,672,611,787,406,831,219,880,1122,599,377,990,362,567,477,387,494,323,700,1029,345,552,959,1044,1066,780,1015,226,1102,223,608,1034,426,548,927,1134,1081,617,939,342,754,1049,525,1003,690,640,1025,872,282,887,414,954,263,993,331,441,1085,951,359,643,1038,370,744,1023,613,1052,864,571,595,497,991,978,1140,231,556,539,891,1010,368,218,1126,588,963,258,632,731,536,214,290,914,1116,315,835,405,273,239,801,506,358,664,400,828,635,474,767,1093,464,1129,644,992,1004,1152,427,803,337,923,543,215,560,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT345+4 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n022.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 14:33:26 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.82/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 8.30/3.33 % [INFO] Parsing done (2488ms).
% 8.30/3.35 % [INFO] Running in sequential loop mode.
% 8.74/3.53 % [INFO] eprover registered as external prover.
% 8.74/3.53 % [INFO] cvc4 registered as external prover.
% 8.74/3.54 % [INFO] Scanning for conjecture ...
% 14.57/5.57 % [INFO] Found a conjecture and 49824 axioms. Running axiom selection ...
% 19.84/8.36 % [INFO] Axiom selection finished. Selected 211 axioms (removed 49613 axioms).
% 20.34/8.53 % [INFO] Problem is first-order (TPTP FOF).
% 20.55/8.54 % [INFO] Type checking passed.
% 20.55/8.55 % [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 ...
% 110.51/28.16 % External prover 'cvc4' found a proof!
% 110.51/28.16 % [INFO] Killing All external provers ...
% 110.65/28.16 % Time passed: 27639ms (effective reasoning time: 24808ms)
% 110.65/28.16 % 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)>
% 110.65/28.17 % Axioms used in derivation (211): dt_k9_conlat_2, fraenkel_a_1_0_domain_1, t10_conlat_2, t27_conlat_1, fc1_zfmisc_1, d1_tarski, t28_conlat_1, t24_conlat_1, t7_subset_1, rc14_conlat_1, fc2_conlat_1, t2_collsp, t3_xboole_1, t43_conlat_1, t34_conlat_1, fc1_xboole_0, t48_domain_1, t40_conlat_1, t8_subset_1, t4_ordinal1, t4_conlat_1, t1_subset, d2_conlat_1, t111_zfmisc_1, dt_k2_subset_1, d5_xboole_0, fc1_conlat_1, t9_measure1, t16_setwiseo, t21_conlat_1, rc1_conlat_1, d8_conlat_1, t1_gate_1, d2_conlat_2, dt_m1_conlat_1, t5_conlat_1, d24_conlat_1, t18_conlat_2, rc6_conlat_1, d17_conlat_1, fraenkel_a_2_1_conlat_1, existence_m2_conlat_1, abstractness_v6_conlat_1, t41_zfmisc_1, t23_conlat_1, t25_conlat_1, t11_conlat_1, t41_conlat_1, rc12_conlat_1, dt_k1_conlat_2, t1_conlat_1, t22_conlat_1, d8_conlat_2, d4_subset_1, involutiveness_k6_relset_1, dt_k2_conlat_2, existence_l3_conlat_1, d1_xboole_0, rc5_conlat_1, d9_conlat_1, t42_conlat_1, d5_conlat_1, dt_m3_conlat_1, t6_boole, dt_k10_conlat_2, rc2_subset_1, t1_xboole_1, d20_conlat_1, t36_conlat_1, d3_conlat_2, t5_subset, rc9_conlat_1, t1_yellow_8, t5_conlat_2, t4_conlat_2, existence_m1_relset_1, t1_zfmisc_1, fc2_subset_1, t79_zfmisc_1, d1_conlat_1, t18_setwiseo, t2_tarski, t37_conlat_1, d14_conlat_1, t5_ordinal1, d13_conlat_1, t4_subset, existence_l2_conlat_1, free_g3_conlat_1, t45_conlat_1, rc4_conlat_1, redefinition_m2_conlat_1, d7_conlat_2, t18_conlat_1, t32_lopclset, t7_boole, t3_ordinal1, rc7_conlat_1, d2_subset_1, t31_conlat_1, fc1_subset_1, t33_zfmisc_1, t7_ordinal1, rc1_subset_1, rc10_conlat_1, d12_conlat_1, dt_k5_conlat_1, t4_subset_1, redefinition_m3_conlat_1, t8_conlat_1, cc2_conlat_1, t3_conlat_1, t2_gate_1, t3_subset, redefinition_k9_conlat_2, t47_conlat_1, dt_g2_conlat_1, t55_subset_1, existence_m1_subset_1, t38_conlat_1, t44_setfam_1, d23_conlat_1, dt_k8_conlat_2, d1_zfmisc_1, l21_conlat_2, fraenkel_a_2_3_conlat_1, dt_k6_conlat_1, rc11_conlat_1, existence_l1_conlat_1, t19_conlat_2, dt_g3_conlat_1, d1_conlat_2, rc1_triang_1, t14_setwiseo, d3_tarski, t6_conlat_1, t2_zf_colla, t39_zfmisc_1, t35_conlat_1, fraenkel_a_1_0_conlat_1, reflexivity_r1_tarski, dt_k7_conlat_2, dt_u4_conlat_1, d18_conlat_1, t6_zfmisc_1, rc3_conlat_1, t10_conlat_1, t2_xboole_1, existence_m3_conlat_1, dt_u5_conlat_1, d16_conlat_1, t9_mcart_1, dt_k12_conlat_1, fc3_conlat_1, t10_subset_1, t26_conlat_1, t2_conlat_1, d15_conlat_1, rc15_conlat_1, t28_finsub_1, fraenkel_a_2_2_conlat_1, t3_hahnban, t26_finsub_1, t80_zfmisc_1, rc16_conlat_1, t24_zfmisc_1, t8_boole, t44_conlat_1, rc1_xboole_0, abstractness_v4_conlat_1, t37_zfmisc_1, t23_finsub_1, t6_conlat_2, t2_subset, existence_m1_conlat_1, dt_m2_conlat_1, t11_conlat_2, t33_conlat_1, t20_conlat_1, d10_xboole_0, t39_conlat_1, t32_finsub_1, t48_subset_1, t9_conlat_2, fraenkel_a_2_0_conlat_1, d11_conlat_1, rc8_conlat_1, t6_ordinal1, d19_conlat_1, redefinition_k8_conlat_1, t49_subset_1, t7_tarski, free_g2_conlat_1, t7_conlat_1, cc1_conlat_1, dt_k7_conlat_1, dt_k8_conlat_1, rc2_xboole_0, t112_zfmisc_1, t9_conlat_1, t13_conlat_2, fraenkel_a_2_0_closure1, dt_k3_conlat_2, dt_l2_conlat_1, t19_conlat_1, t63_subset_1, rc13_conlat_1, antisymmetry_r2_hidden, t17_conlat_2, rc2_conlat_1, t1_closure1
% 110.65/28.17 % No. of inferences in proof: 470
% 110.65/28.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27639 ms resp. 24808 ms w/o parsing
% 110.77/28.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 110.77/28.32 % [INFO] Killing All external provers ...
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