TSTP Solution File: LAT366+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT366+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:28:07 EDT 2023
% Result : Theorem 109.10s 22.22s
% Output : Refutation 109.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 228
% Syntax : Number of formulae : 381 ( 13 unt; 77 typ; 0 def)
% Number of atoms : 2580 ( 34 equ; 0 cnn)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 8335 ( 296 ~; 2 |;1785 &;5763 @)
% ( 6 <=>; 483 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 141 ( 141 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 77 usr; 2 con; 0-4 aty)
% Number of variables : 607 ( 0 ^; 541 !; 66 ?; 607 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_orders_2_type,type,
v2_orders_2: $i > $o ).
thf(v3_orders_2_type,type,
v3_orders_2: $i > $o ).
thf(v4_orders_2_type,type,
v4_orders_2: $i > $o ).
thf(v1_lattice3_type,type,
v1_lattice3: $i > $o ).
thf(v2_lattice3_type,type,
v2_lattice3: $i > $o ).
thf(v3_lattice3_type,type,
v3_lattice3: $i > $o ).
thf(l1_orders_2_type,type,
l1_orders_2: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v8_waybel_1_type,type,
v8_waybel_1: $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v22_waybel_0_type,type,
v22_waybel_0: $i > $i > $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k2_yellow_2_type,type,
k2_yellow_2: $i > $i > $i > $i ).
thf(r1_waybel_3_type,type,
r1_waybel_3: $i > $i > $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g1_orders_2_type,type,
g1_orders_2: $i > $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k8_relat_1_type,type,
k8_relat_1: $i > $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(v1_orders_2_type,type,
v1_orders_2: $i > $o ).
thf(u1_orders_2_type,type,
u1_orders_2: $i > $i ).
thf(m1_yellow_0_type,type,
m1_yellow_0: $i > $i > $o ).
thf(v7_yellow_0_type,type,
v7_yellow_0: $i > $i > $o ).
thf(v18_waybel_0_type,type,
v18_waybel_0: $i > $i > $i > $o ).
thf(k2_waybel34_type,type,
k2_waybel34: $i > $i > $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v17_waybel_0_type,type,
v17_waybel_0: $i > $i > $i > $o ).
thf(v19_waybel_0_type,type,
v19_waybel_0: $i > $i > $i > $o ).
thf(v21_waybel_0_type,type,
v21_waybel_0: $i > $i > $i > $o ).
thf(v4_waybel_1_type,type,
v4_waybel_1: $i > $i > $i > $o ).
thf(v5_orders_3_type,type,
v5_orders_3: $i > $i > $i > $o ).
thf(v6_waybel_1_type,type,
v6_waybel_1: $i > $i > $o ).
thf(v11_quantal1_type,type,
v11_quantal1: $i > $o ).
thf(k2_waybel_1_type,type,
k2_waybel_1: $i > $i > $i > $i ).
thf(k3_waybel_1_type,type,
k3_waybel_1: $i > $i > $i > $i ).
thf(k1_waybel34_type,type,
k1_waybel34: $i > $i > $i > $i ).
thf(v20_waybel_0_type,type,
v20_waybel_0: $i > $i > $i > $o ).
thf(v1_xcmplx_0_type,type,
v1_xcmplx_0: $i > $o ).
thf(v4_ordinal2_type,type,
v4_ordinal2: $i > $o ).
thf(v1_xreal_0_type,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_type,type,
v1_rat_1: $i > $o ).
thf(v5_yellow_0_type,type,
v5_yellow_0: $i > $i > $o ).
thf(v6_yellow_0_type,type,
v6_yellow_0: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v2_yellow_0_type,type,
v2_yellow_0: $i > $o ).
thf(v24_waybel_0_type,type,
v24_waybel_0: $i > $o ).
thf(v25_waybel_0_type,type,
v25_waybel_0: $i > $o ).
thf(v1_yellow_0_type,type,
v1_yellow_0: $i > $o ).
thf(v3_yellow_0_type,type,
v3_yellow_0: $i > $o ).
thf(v4_yellow_0_type,type,
v4_yellow_0: $i > $i > $o ).
thf(k7_grcat_1_type,type,
k7_grcat_1: $i > $i ).
thf(v23_waybel_0_type,type,
v23_waybel_0: $i > $i > $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v7_waybel_1_type,type,
v7_waybel_1: $i > $i > $o ).
thf(v3_waybel_0_type,type,
v3_waybel_0: $i > $i > $o ).
thf(v4_waybel_0_type,type,
v4_waybel_0: $i > $i > $o ).
thf(k7_yellow_2_type,type,
k7_yellow_2: $i > $i > $i > $i > $i ).
thf(v8_yellow_0_type,type,
v8_yellow_0: $i > $i > $o ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(v5_waybel_1_type,type,
v5_waybel_1: $i > $i > $i > $o ).
thf(v2_funct_2_type,type,
v2_funct_2: $i > $i > $i > $o ).
thf(v1_waybel34_type,type,
v1_waybel34: $i > $i > $i > $o ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(645,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(130,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k2_waybel_1 @ A @ B @ C )
= ( k8_relat_1 @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_waybel_1) ).
thf(809,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k2_waybel_1 @ A @ B @ C )
= ( k8_relat_1 @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(100,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_yellow_0) ).
thf(666,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(68,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A ) )
=> ( v3_yellow_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(481,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A ) )
=> ( v3_yellow_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(79,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_1) ).
thf(523,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(14,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(217,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v2_funct_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ ( k3_waybel_1 @ A @ B @ C ) @ ( k2_yellow_2 @ A @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel_1) ).
thf(873,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v2_funct_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ ( k3_waybel_1 @ A @ B @ C ) @ ( k2_yellow_2 @ A @ B @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(379,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(28,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(269,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(51,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(384,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A )
& ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v24_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v25_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel34) ).
thf(913,plain,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A )
& ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v24_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v25_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_waybel_1) ).
thf(930,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k3_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(101,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(670,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(81,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v4_yellow_0 @ B @ A )
=> ( ( v2_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_yellow_0) ).
thf(538,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v4_yellow_0 @ B @ A )
=> ( ( v2_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v22_waybel_0 @ B @ A @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) ) )
=> ( ( ( E = C )
& ( F = D ) )
=> ( ( r1_waybel_3 @ A @ C @ D )
<=> ( r1_waybel_3 @ ( k2_yellow_2 @ A @ A @ B ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_waybel34) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v22_waybel_0 @ B @ A @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) ) )
=> ( ( ( E = C )
& ( F = D ) )
=> ( ( r1_waybel_3 @ A @ C @ D )
<=> ( r1_waybel_3 @ ( k2_yellow_2 @ A @ A @ B ) @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(153,plain,
~ ! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v22_waybel_0 @ B @ A @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) ) )
=> ( ( ( E = C )
& ( F = D ) )
=> ( ( ( r1_waybel_3 @ A @ C @ D )
=> ( r1_waybel_3 @ ( k2_yellow_2 @ A @ A @ B ) @ E @ F ) )
& ( ( r1_waybel_3 @ ( k2_yellow_2 @ A @ A @ B ) @ E @ F )
=> ( r1_waybel_3 @ A @ C @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,axiom,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v3_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_8) ).
thf(404,plain,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v3_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v23_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_waybel_0) ).
thf(885,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v23_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(39,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(320,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(53,axiom,
? [A: $i] : ( l1_orders_2 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(389,plain,
? [A: $i] : ( l1_orders_2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(85,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(570,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)],[85]) ).
thf(6,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(184,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_membered @ k1_xboole_0 )
& ( v2_membered @ k1_xboole_0 )
& ( v3_membered @ k1_xboole_0 )
& ( v4_membered @ k1_xboole_0 )
& ( v5_membered @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(75,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A )
& ( v7_waybel_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_1) ).
thf(504,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A )
& ( v7_waybel_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(150,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v22_waybel_0 @ C @ A @ B )
=> ( v1_waybel34 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_waybel34) ).
thf(934,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v22_waybel_0 @ C @ A @ B )
=> ( v1_waybel34 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(357,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(32,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v17_waybel_0 @ ( k2_waybel_1 @ A @ A @ B ) @ A @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v18_waybel_0 @ ( k3_waybel_1 @ A @ A @ B ) @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( ( k1_waybel34 @ A @ ( k2_yellow_2 @ A @ A @ B ) @ ( k2_waybel_1 @ A @ A @ B ) )
= ( k3_waybel_1 @ A @ A @ B ) )
& ( ( k2_waybel34 @ A @ ( k2_yellow_2 @ A @ A @ B ) @ ( k3_waybel_1 @ A @ A @ B ) )
= ( k2_waybel_1 @ A @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_waybel34) ).
thf(284,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v17_waybel_0 @ ( k2_waybel_1 @ A @ A @ B ) @ A @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v18_waybel_0 @ ( k3_waybel_1 @ A @ A @ B ) @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( ( k1_waybel34 @ A @ ( k2_yellow_2 @ A @ A @ B ) @ ( k2_waybel_1 @ A @ A @ B ) )
= ( k3_waybel_1 @ A @ A @ B ) )
& ( ( k2_waybel34 @ A @ ( k2_yellow_2 @ A @ A @ B ) @ ( k3_waybel_1 @ A @ A @ B ) )
= ( k2_waybel_1 @ A @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(143,axiom,
! [A: $i] :
( ( ( v1_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_waybel_8) ).
thf(881,plain,
! [A: $i] :
( ( ( v1_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(19,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(228,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(316,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(117,axiom,
! [A: $i] :
( ( ( v4_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v4_yellow_0 @ B @ A )
=> ( ( v4_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_yellow_0) ).
thf(756,plain,
! [A: $i] :
( ( ( v4_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v4_yellow_0 @ B @ A )
=> ( ( v4_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(66,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v11_quantal1 @ ( k7_grcat_1 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v17_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v18_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v19_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v20_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v21_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v22_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v7_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v8_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel10) ).
thf(443,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v11_quantal1 @ ( k7_grcat_1 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v17_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v18_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v19_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v20_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v21_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v22_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v7_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v8_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(48,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(376,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(135,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_waybel34 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_waybel_3 @ A @ D @ E )
=> ( r1_waybel_3 @ B @ ( k7_yellow_2 @ ( u1_struct_0 @ A ) @ B @ C @ D ) @ ( k7_yellow_2 @ ( u1_struct_0 @ A ) @ B @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_waybel34) ).
thf(834,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v1_waybel34 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_waybel_3 @ A @ D @ E )
=> ( r1_waybel_3 @ B @ ( k7_yellow_2 @ ( u1_struct_0 @ A ) @ B @ C @ D ) @ ( k7_yellow_2 @ ( u1_struct_0 @ A ) @ B @ C @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_waybel_3 @ A @ D @ E )
=> ( r1_waybel_3 @ B @ ( k7_yellow_2 @ ( u1_struct_0 @ A ) @ B @ C @ D ) @ ( k7_yellow_2 @ ( u1_struct_0 @ A ) @ B @ C @ E ) ) ) ) )
=> ( v1_waybel34 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(56,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(397,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(141,axiom,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v2_lattice3 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_yellow_0) ).
thf(866,plain,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v2_lattice3 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(24,axiom,
! [A: $i] :
( ( ( v4_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel_8) ).
thf(243,plain,
! [A: $i] :
( ( ( v4_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v18_waybel_0 @ C @ B @ A )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_relat_1 @ ( k2_waybel34 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k2_waybel34 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k2_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v19_waybel_0 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v21_waybel_0 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v4_waybel_1 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v5_orders_3 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel34) ).
thf(248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v18_waybel_0 @ C @ B @ A )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_relat_1 @ ( k2_waybel34 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k2_waybel34 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k2_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v19_waybel_0 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v21_waybel_0 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v4_waybel_1 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B )
& ( v5_orders_3 @ ( k2_waybel34 @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(119,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(761,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)],[119]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(381,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(15,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(220,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(115,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v8_yellow_0 @ B @ A )
=> ( v4_waybel_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_0) ).
thf(746,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v8_yellow_0 @ B @ A )
=> ( v4_waybel_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(122,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v7_yellow_0 @ B @ A )
=> ( v3_waybel_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel_0) ).
thf(778,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v7_yellow_0 @ B @ A )
=> ( v3_waybel_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(140,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(862,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(84,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A )
& ( v7_yellow_0 @ B @ A )
& ( v8_yellow_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_yellow_0) ).
thf(561,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A )
& ( v7_yellow_0 @ B @ A )
& ( v8_yellow_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(59,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_1) ).
thf(407,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(30,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(275,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( m2_relset_1 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_waybel_1) ).
thf(815,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( m2_relset_1 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_2) ).
thf(830,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v7_waybel_1 @ B @ A )
& ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v5_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v7_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v3_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel10) ).
thf(551,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v7_waybel_1 @ B @ A )
& ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v5_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v7_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v3_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(40,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v22_waybel_0 @ B @ A @ A )
<=> ( v22_waybel_0 @ ( k2_waybel_1 @ A @ A @ B ) @ A @ ( k2_yellow_2 @ A @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_waybel34) ).
thf(324,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v22_waybel_0 @ B @ A @ A )
=> ( v22_waybel_0 @ ( k2_waybel_1 @ A @ A @ B ) @ A @ ( k2_yellow_2 @ A @ A @ B ) ) )
& ( ( v22_waybel_0 @ ( k2_waybel_1 @ A @ A @ B ) @ A @ ( k2_yellow_2 @ A @ A @ B ) )
=> ( v22_waybel_0 @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(224,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(114,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(742,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(107,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A )
& ( v7_yellow_0 @ B @ A )
& ( v8_yellow_0 @ B @ A )
& ( v3_waybel_0 @ B @ A )
& ( v4_waybel_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_0) ).
thf(697,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A )
& ( v7_yellow_0 @ B @ A )
& ( v8_yellow_0 @ B @ A )
& ( v3_waybel_0 @ B @ A )
& ( v4_waybel_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel10) ).
thf(420,plain,
! [A: $i,B: $i] :
( ( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
& ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(499,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
& ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(70,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(488,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(146,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v7_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v8_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_1) ).
thf(901,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v7_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v8_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(90,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v8_yellow_0 @ B @ A )
=> ~ ( v3_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_waybel10) ).
thf(590,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v8_yellow_0 @ B @ A )
=> ~ ( v3_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(103,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A )
& ( v8_waybel_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_1) ).
thf(679,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A )
& ( v8_waybel_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(55,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(393,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(99,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v11_quantal1 @ B )
& ( v5_orders_3 @ B @ A @ A )
& ( v17_waybel_0 @ B @ A @ A )
& ( v18_waybel_0 @ B @ A @ A )
& ( v19_waybel_0 @ B @ A @ A )
& ( v20_waybel_0 @ B @ A @ A )
& ( v21_waybel_0 @ B @ A @ A )
& ( v22_waybel_0 @ B @ A @ A )
& ( v6_waybel_1 @ B @ A )
& ( v7_waybel_1 @ B @ A )
& ( v8_waybel_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel10) ).
thf(647,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v11_quantal1 @ B )
& ( v5_orders_3 @ B @ A @ A )
& ( v17_waybel_0 @ B @ A @ A )
& ( v18_waybel_0 @ B @ A @ A )
& ( v19_waybel_0 @ B @ A @ A )
& ( v20_waybel_0 @ B @ A @ A )
& ( v21_waybel_0 @ B @ A @ A )
& ( v22_waybel_0 @ B @ A @ A )
& ( v6_waybel_1 @ B @ A )
& ( v7_waybel_1 @ B @ A )
& ( v8_waybel_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(110,axiom,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(721,plain,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(37,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ( v1_orders_2 @ B )
& ( v5_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice5) ).
thf(311,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ( v1_orders_2 @ B )
& ( v5_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(82,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel_1) ).
thf(541,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(102,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(674,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(126,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( l1_orders_2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(794,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( l1_orders_2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v19_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel21) ).
thf(586,plain,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v19_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(60,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v3_yellow_0 @ A )
=> ( ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(412,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v3_yellow_0 @ A )
=> ( ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(76,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(513,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(138,axiom,
! [A: $i] :
( ( ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v2_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_waybel_8) ).
thf(856,plain,
! [A: $i] :
( ( ( v2_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v2_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(111,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_orders_2 @ A )
=> ( A
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(733,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_orders_2 @ A )
=> ( A
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(88,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(584,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(133,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v24_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(819,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v24_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(106,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_8) ).
thf(694,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(7,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(191,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v22_waybel_0 @ C @ A @ B ) )
=> ( ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel17) ).
thf(772,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v22_waybel_0 @ C @ A @ B ) )
=> ( ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k1_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel34) ).
thf(291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k1_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(259,plain,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(54,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(391,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_yellow_0 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B )
& ( v20_waybel_0 @ C @ A @ B )
& ( v22_waybel_0 @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_9) ).
thf(936,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_yellow_0 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B )
& ( v20_waybel_0 @ C @ A @ B )
& ( v22_waybel_0 @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v19_waybel_0 @ C @ A @ B )
& ( v20_waybel_0 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice5) ).
thf(335,plain,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v19_waybel_0 @ C @ A @ B )
& ( v20_waybel_0 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(236,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(129,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(804,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(94,axiom,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(611,plain,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v2_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v1_partfun1 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_1) ).
thf(787,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v2_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v1_partfun1 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v4_waybel_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( v19_waybel_0 @ C @ A @ B )
& ( v21_waybel_0 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel_1) ).
thf(764,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v4_waybel_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( v19_waybel_0 @ C @ A @ B )
& ( v21_waybel_0 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(124,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_lattice3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(784,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_lattice3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(112,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(736,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(20,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(230,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ ( k2_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_waybel34) ).
thf(271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ ( k2_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k2_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(145,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v7_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_1) ).
thf(890,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ~ ( v1_xboole_0 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v5_orders_3 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v23_waybel_0 @ ( k7_grcat_1 @ A ) @ A @ A )
& ( v6_waybel_1 @ ( k7_grcat_1 @ A ) @ A )
& ( v7_waybel_1 @ ( k7_grcat_1 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(71,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
=> ( ( k7_yellow_2 @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ B @ ( k3_waybel_1 @ A @ B @ C ) @ D )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_waybel_1) ).
thf(494,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
=> ( ( k7_yellow_2 @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) @ B @ ( k3_waybel_1 @ A @ B @ C ) @ D )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(13,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(213,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(69,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel10) ).
thf(483,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_relat_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v2_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(78,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(520,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v22_waybel_0 @ B @ A @ A )
& ( v7_waybel_1 @ B @ A )
& ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v5_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v7_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v3_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v4_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_waybel10) ).
thf(626,plain,
! [A: $i,B: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v22_waybel_0 @ B @ A @ A )
& ( v7_waybel_1 @ B @ A )
& ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v2_lattice3 @ ( k2_yellow_2 @ A @ A @ B ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v5_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v7_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v3_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A )
& ( v4_waybel_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(67,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_yellow_0 @ B )
& ( v2_yellow_0 @ B )
& ( v3_yellow_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A )
& ( v7_yellow_0 @ B @ A )
& ( v3_waybel_0 @ B @ A )
& ( v4_waybel_0 @ B @ A )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel21) ).
thf(462,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_yellow_0 @ B )
& ( v2_yellow_0 @ B )
& ( v3_yellow_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v5_yellow_0 @ B @ A )
& ( v7_yellow_0 @ B @ A )
& ( v3_waybel_0 @ B @ A )
& ( v4_waybel_0 @ B @ A )
& ( v24_waybel_0 @ B )
& ( v25_waybel_0 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v19_waybel_0 @ C @ A @ B )
& ( v21_waybel_0 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_waybel_0) ).
thf(399,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v19_waybel_0 @ C @ A @ B )
& ( v21_waybel_0 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(123,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_8) ).
thf(780,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(18,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(226,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(65,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel_8) ).
thf(438,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
& ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(23,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(241,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(80,axiom,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_yellow_0) ).
thf(531,plain,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v6_yellow_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(374,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(131,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(812,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(43,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_yellow_0 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_2) ).
thf(342,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_yellow_0 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_yellow_0 @ A )
& ( v2_yellow_0 @ A )
& ( v3_yellow_0 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(355,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,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(194,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(97,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_0) ).
thf(640,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ? [B: $i] :
( ( m1_yellow_0 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v20_waybel_0 @ C @ A @ B )
& ( v22_waybel_0 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_waybel_0) ).
thf(295,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v20_waybel_0 @ C @ A @ B )
& ( v22_waybel_0 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(41,axiom,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v3_lattice3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(327,plain,
? [A: $i] :
( ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_orders_2 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v3_lattice3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(182,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k7_yellow_2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_yellow_2) ).
thf(502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k7_yellow_2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v2_yellow_0 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( v19_waybel_0 @ C @ A @ B )
& ( v21_waybel_0 @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_yellow_9) ).
thf(840,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v2_yellow_0 @ B )
& ( l1_orders_2 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( v19_waybel_0 @ C @ A @ B )
& ( v21_waybel_0 @ C @ A @ B )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v2_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v3_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B )
& ( v24_waybel_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v25_waybel_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_lattice3 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v2_lattice3 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v3_lattice3 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_waybel34) ).
thf(359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v3_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v2_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v3_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v2_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v3_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B )
& ( v24_waybel_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v25_waybel_0 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v1_lattice3 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v2_lattice3 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v3_lattice3 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(386,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v8_yellow_0 @ B @ A )
=> ( v6_yellow_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_yellow_0) ).
thf(497,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v8_yellow_0 @ B @ A )
=> ( v6_yellow_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(203,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(104,axiom,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v4_yellow_0 @ B @ A )
=> ( ( v3_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_yellow_0) ).
thf(688,plain,
! [A: $i] :
( ( ( v3_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v4_yellow_0 @ B @ A )
=> ( ( v3_orders_2 @ B )
& ( v4_yellow_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(87,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v7_waybel_1 @ B @ A )
=> ( v7_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) )
& ( ( v8_waybel_1 @ B @ A )
=> ( v8_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_waybel_1) ).
thf(581,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v7_waybel_1 @ B @ A )
=> ( v7_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) )
& ( ( v8_waybel_1 @ B @ A )
=> ( v8_yellow_0 @ ( k2_yellow_2 @ A @ A @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(118,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(759,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k7_yellow_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_yellow_2) ).
thf(517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ A @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k7_yellow_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v2_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v1_partfun1 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v5_orders_3 @ ( k2_waybel_1 @ A @ B @ C ) @ A @ ( k2_yellow_2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel10) ).
thf(748,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_orders_3 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k2_waybel_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k2_waybel_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v2_funct_2 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v1_partfun1 @ ( k2_waybel_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k2_yellow_2 @ A @ B @ C ) ) )
& ( v5_orders_3 @ ( k2_waybel_1 @ A @ B @ C ) @ A @ ( k2_yellow_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(152,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(946,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(25,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v7_yellow_0 @ B @ A )
=> ~ ( v3_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel10) ).
thf(246,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v7_yellow_0 @ B @ A )
=> ~ ( v3_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(64,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_lattice3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(433,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_lattice3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v24_waybel_0 @ A )
& ( v25_waybel_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(109,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(716,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(128,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_lattice3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(800,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_lattice3 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(300,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(92,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v1_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(603,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v1_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(305,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v4_ordinal2 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(210,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(239,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B )
& ( m1_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_2) ).
thf(796,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_orders_2 @ ( k2_yellow_2 @ A @ B @ C ) )
& ( v4_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B )
& ( m1_yellow_0 @ ( k2_yellow_2 @ A @ B @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(148,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] : ( m1_yellow_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(928,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] : ( m1_yellow_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(61,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v2_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v24_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(415,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v2_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v24_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(113,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(740,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(86,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v7_waybel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_waybel_1) ).
thf(575,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v7_waybel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(63,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_yellow_0 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_yellow_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(427,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v2_yellow_0 @ A )
& ( v25_waybel_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_yellow_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(139,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v7_yellow_0 @ B @ A )
=> ( v5_yellow_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_yellow_0) ).
thf(860,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_yellow_0 @ B @ A )
=> ( ( v7_yellow_0 @ B @ A )
=> ( v5_yellow_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(137,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_1) ).
thf(850,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v8_waybel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(3,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(178,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(93,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v8_yellow_0 @ B @ A )
& ( m1_yellow_0 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( r1_waybel_3 @ A @ C @ D ) )
=> ( r1_waybel_3 @ B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_waybel34) ).
thf(607,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v4_yellow_0 @ B @ A )
& ( v8_yellow_0 @ B @ A )
& ( m1_yellow_0 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( r1_waybel_3 @ A @ C @ D ) )
=> ( r1_waybel_3 @ B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(31,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v11_quantal1 @ B )
& ( v5_orders_3 @ B @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel10) ).
thf(277,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v6_waybel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ B )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v11_quantal1 @ B )
& ( v5_orders_3 @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(105,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k3_waybel_1 @ A @ B @ C )
= ( k7_grcat_1 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_waybel_1) ).
thf(691,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k3_waybel_1 @ A @ B @ C )
= ( k7_grcat_1 @ ( k2_yellow_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(222,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_waybel34 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k1_waybel34 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k1_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v18_waybel_0 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A )
& ( v20_waybel_0 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A )
& ( v22_waybel_0 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A )
& ( v5_waybel_1 @ ( k1_waybel34 @ A @ B @ C ) @ A @ B )
& ( v5_orders_3 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel34) ).
thf(592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v1_lattice3 @ A )
& ( v2_lattice3 @ A )
& ( v3_lattice3 @ A )
& ( l1_orders_2 @ A )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( v1_lattice3 @ B )
& ( v2_lattice3 @ B )
& ( v3_lattice3 @ B )
& ( l1_orders_2 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v17_waybel_0 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_waybel34 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k1_waybel34 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ ( k1_waybel34 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( k1_waybel34 @ A @ B @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v18_waybel_0 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A )
& ( v20_waybel_0 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A )
& ( v22_waybel_0 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A )
& ( v5_waybel_1 @ ( k1_waybel34 @ A @ B @ C ) @ A @ B )
& ( v5_orders_3 @ ( k1_waybel34 @ A @ B @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_waybel_1 @ C @ B @ A ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B )
& ( v20_waybel_0 @ C @ A @ B )
& ( v22_waybel_0 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_1) ).
thf(708,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( l1_orders_2 @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_orders_2 @ B )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B )
& ( l1_orders_2 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v5_waybel_1 @ C @ B @ A ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v18_waybel_0 @ C @ A @ B )
& ( v20_waybel_0 @ C @ A @ B )
& ( v22_waybel_0 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(6629,plain,
$false,
inference(cvc4,[status(thm)],[645,809,666,481,523,217,873,379,269,384,913,930,670,538,153,404,885,320,389,570,184,504,196,934,357,638,284,881,228,316,756,443,376,834,397,866,243,248,201,761,381,220,746,778,862,561,407,275,815,830,551,324,224,742,697,420,499,488,901,590,679,393,647,721,311,541,674,794,586,412,513,856,180,733,584,819,694,191,772,291,259,391,936,335,236,804,611,787,764,784,736,230,271,890,494,213,483,520,626,462,399,780,226,438,241,531,374,812,342,355,194,640,295,327,182,502,840,359,386,497,203,688,581,759,517,748,946,246,433,716,800,300,603,305,210,239,796,928,415,740,575,427,860,850,178,607,277,691,222,592,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT366+1 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 14:37:25 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.05 % [INFO] Parsing done (195ms).
% 1.51/1.05 % [INFO] Running in sequential loop mode.
% 2.31/1.31 % [INFO] eprover registered as external prover.
% 2.31/1.31 % [INFO] cvc4 registered as external prover.
% 2.31/1.31 % [INFO] Scanning for conjecture ...
% 2.51/1.44 % [INFO] Found a conjecture and 158 axioms. Running axiom selection ...
% 3.12/1.54 % [INFO] Axiom selection finished. Selected 150 axioms (removed 8 axioms).
% 3.51/1.70 % [INFO] Problem is first-order (TPTP FOF).
% 3.68/1.71 % [INFO] Type checking passed.
% 3.68/1.71 % [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 ...
% 109.10/22.22 % External prover 'cvc4' found a proof!
% 109.10/22.22 % [INFO] Killing All external provers ...
% 109.10/22.22 % Time passed: 21705ms (effective reasoning time: 21162ms)
% 109.10/22.22 % 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)>
% 109.10/22.22 % Axioms used in derivation (150): rc1_membered, cc15_membered, dt_l1_orders_2, fc10_waybel34, redefinition_m2_relset_1, dt_k7_grcat_1, cc12_membered, cc1_waybel17, rc4_yellow_9, cc2_finset_1, cc1_waybel21, fc3_waybel_1, fc4_waybel10, dt_k1_waybel34, dt_k2_waybel_1, fc9_waybel34, cc7_waybel_0, fc10_waybel_8, fc3_waybel10, rc4_finset_1, cc10_membered, t1_subset, rc2_waybel10, rc1_waybel21, rc2_yellow_0, fc5_waybel_1, fc2_yellow_2, rc1_waybel10, fc4_waybel_1, cc12_waybel_0, rc3_funct_1, rc3_waybel_1, cc1_waybel_0, cc1_lattice3, dt_m2_relset_1, rc3_yellow_0, cc14_waybel_0, cc11_waybel_0, rc13_waybel_0, rc1_funct_1, dt_u1_orders_2, cc3_waybel_1, rc1_lattice3, fc8_waybel_8, fc6_waybel_8, t36_waybel34, cc2_waybel_0, rc2_lattice3, t6_boole, fc2_waybel34, t5_subset, cc9_waybel_0, cc19_membered, existence_m1_relset_1, fc7_waybel_8, d16_waybel_1, cc9_yellow_0, cc11_yellow_0, fc6_membered, t33_waybel34, cc11_membered, t4_subset, fc9_waybel_8, dt_k2_yellow_2, cc2_waybel_1, rc5_yellow_0, d17_waybel_1, dt_k7_yellow_2, cc20_membered, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, fc1_waybel34, fc5_funct_1, cc12_yellow_0, cc13_waybel_0, dt_g1_orders_2, cc3_waybel10, rc2_funct_1, cc4_membered, t34_waybel_1, cc1_yellow_2, rc3_yellow_9, cc1_waybel10, cc6_yellow_0, cc18_membered, abstractness_v1_orders_2, cc4_yellow_0, rc3_waybel_0, fc10_waybel10, rc2_lattice5, cc10_yellow_0, cc2_funct_1, t24_waybel34, t3_subset, cc1_relset_1, cc13_membered, d8_waybel34, existence_m1_subset_1, cc2_waybel10, dt_k8_relat_1, rc1_waybel_1, fc15_waybel10, existence_m2_relset_1, t34_waybel34, free_g1_orders_2, fc1_struct_0, cc7_yellow_0, rc4_yellow_0, reflexivity_r1_tarski, redefinition_k7_yellow_2, fc2_waybel_1, rc2_waybel_1, cc17_membered, cc10_waybel_0, existence_m1_yellow_0, rc3_finset_1, cc6_waybel_0, dt_m1_yellow_0, cc5_yellow_0, rc1_finset_1, cc1_finset_1, cc4_waybel_1, cc1_yellow_0, t8_boole, t56_waybel_1, fc4_waybel_8, rc5_struct_0, t2_subset, cc1_membered, dt_k3_waybel_1, fc2_waybel10, cc8_waybel_0, cc2_membered, cc2_lattice3, cc3_membered, cc14_membered, fc6_waybel_1, existence_l1_struct_0, cc8_yellow_0, cc16_membered, rc1_lattice5, dt_k2_waybel34, fc14_finset_1, cc3_yellow_0, cc1_waybel_1, fc5_waybel_8, antisymmetry_r2_hidden, fc7_waybel_1
% 109.10/22.22 % No. of inferences in proof: 304
% 109.10/22.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21705 ms resp. 21162 ms w/o parsing
% 109.54/22.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 109.54/22.35 % [INFO] Killing All external provers ...
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