%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT356+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:28 AM UTC 2026
% Result : Theorem 12.73s 4.21s
% Output : Refutation 13.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 84
% Syntax : Number of formulae : 170 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 1450 ( 18 equ; 0 cnn)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 4521 ( 172 ~; 2 |;1046 &;3069 @)
% ( 3 <=>; 229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 2 con; 0-4 aty)
% Number of variables : 327 ( 0 ^; 277 !; 50 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_orders_2_decl,type,
v2_orders_2: $i > $o ).
thf(v3_orders_2_decl,type,
v3_orders_2: $i > $o ).
thf(v4_orders_2_decl,type,
v4_orders_2: $i > $o ).
thf(v1_lattice3_decl,type,
v1_lattice3: $i > $o ).
thf(v2_lattice3_decl,type,
v2_lattice3: $i > $o ).
thf(v3_lattice3_decl,type,
v3_lattice3: $i > $o ).
thf(l1_orders_2_decl,type,
l1_orders_2: $i > $o ).
thf(k1_waybel34_decl,type,
k1_waybel34: $i > $i > $i > $i ).
thf(k7_grcat_1_decl,type,
k7_grcat_1: $i > $i ).
thf(k2_waybel34_decl,type,
k2_waybel34: $i > $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(v6_waybel_1_decl,type,
v6_waybel_1: $i > $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v11_quantal1_decl,type,
v11_quantal1: $i > $o ).
thf(v5_orders_3_decl,type,
v5_orders_3: $i > $i > $i > $o ).
thf(v18_waybel_0_decl,type,
v18_waybel_0: $i > $i > $i > $o ).
thf(v20_waybel_0_decl,type,
v20_waybel_0: $i > $i > $i > $o ).
thf(v22_waybel_0_decl,type,
v22_waybel_0: $i > $i > $i > $o ).
thf(v19_waybel_0_decl,type,
v19_waybel_0: $i > $i > $i > $o ).
thf(v2_yellow_0_decl,type,
v2_yellow_0: $i > $o ).
thf(v24_waybel_0_decl,type,
v24_waybel_0: $i > $o ).
thf(v25_waybel_0_decl,type,
v25_waybel_0: $i > $o ).
thf(v1_yellow_0_decl,type,
v1_yellow_0: $i > $o ).
thf(v3_yellow_0_decl,type,
v3_yellow_0: $i > $o ).
thf(v17_waybel_0_decl,type,
v17_waybel_0: $i > $i > $i > $o ).
thf(v21_waybel_0_decl,type,
v21_waybel_0: $i > $i > $i > $o ).
thf(v23_waybel_0_decl,type,
v23_waybel_0: $i > $i > $i > $o ).
thf(v7_waybel_1_decl,type,
v7_waybel_1: $i > $i > $o ).
thf(v8_waybel_1_decl,type,
v8_waybel_1: $i > $i > $o ).
thf(v5_waybel_1_decl,type,
v5_waybel_1: $i > $i > $i > $o ).
thf(v3_waybel_1_decl,type,
v3_waybel_1: $i > $i > $i > $o ).
thf(k1_waybel_1_decl,type,
k1_waybel_1: $i > $i > $i > $i > $i ).
thf(v4_waybel_1_decl,type,
v4_waybel_1: $i > $i > $i > $o ).
thf(m1_waybel_1_decl,type,
m1_waybel_1: $i > $i > $i > $o ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(74,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(472,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(188,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ ( A @ k7_grcat_1 @ ( A @ k7_grcat_1 @ ( A @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_waybel34) ).
thf(365,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ ( A @ k7_grcat_1 @ ( A @ k7_grcat_1 @ ( A @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_1) ).
thf(249,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v23_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_waybel_0) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v23_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(28,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(170,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v7_waybel_1 ) )
& ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_1) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v7_waybel_1 ) )
& ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(120,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(174,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v18_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_9) ).
thf(565,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v18_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_1) ).
thf(492,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(30,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(179,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v4_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel17) ).
thf(376,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v4_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(76,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ v3_lattice3 )
& ( A @ v3_lattice3 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k1_waybel34 ) ) ) )
<=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_waybel34) ).
thf(485,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ v3_lattice3 )
& ( A @ v3_lattice3 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) )
=> ( D
= ( C @ ( B @ ( A @ k1_waybel34 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k1_waybel34 ) ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v8_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v7_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v22_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v21_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v20_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v19_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v18_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v17_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ k7_grcat_1 @ v11_quantal1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel10) ).
thf(280,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v8_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v7_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v22_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v21_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v20_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v19_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v18_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v17_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ k7_grcat_1 @ v11_quantal1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_waybel_0) ).
thf(243,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel10) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel10) ).
thf(302,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(160,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_lattice3 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v3_waybel_1 ) ) )
& ( B @ ( A @ ( C @ m1_waybel_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel34) ).
thf(561,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_lattice3 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v3_waybel_1 ) ) )
& ( B @ ( A @ ( C @ m1_waybel_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(392,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(97,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ v7_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_waybel_1) ).
thf(329,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ v7_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_waybel34) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(134,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v3_lattice3 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v5_orders_3 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v5_waybel_1 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v22_waybel_0 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v20_waybel_0 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_2 ) ) )
& ~ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_xboole_0 )
& ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel34) ).
thf(343,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v3_lattice3 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v5_orders_3 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v5_waybel_1 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v22_waybel_0 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v20_waybel_0 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_2 ) ) )
& ~ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_xboole_0 )
& ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(105,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ( A @ k7_grcat_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(360,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ( A @ k7_grcat_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) @ m1_waybel_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel_1) ).
thf(398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) @ m1_waybel_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_yellow_9) ).
thf(412,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v7_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_1) ).
thf(430,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v7_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(26,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(166,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(149,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ v8_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_1) ).
thf(423,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ v8_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(191,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(118,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(259,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(81,axiom,
? [A: $i] :
( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(540,plain,
? [A: $i] :
( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( ( A @ k7_grcat_1 @ ( A @ ( A @ k2_waybel34 ) ) )
= ( A @ k7_grcat_1 ) )
& ( ( A @ k7_grcat_1 @ ( A @ ( A @ k1_waybel34 ) ) )
= ( A @ k7_grcat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_waybel34) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( ( A @ k7_grcat_1 @ ( A @ ( A @ k2_waybel34 ) ) )
= ( A @ k7_grcat_1 ) )
& ( ( A @ k7_grcat_1 @ ( A @ ( A @ k1_waybel34 ) ) )
= ( A @ k7_grcat_1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(86,plain,
~ ! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( ( A @ k7_grcat_1 @ ( A @ ( A @ k2_waybel34 ) ) )
= ( A @ k7_grcat_1 ) )
& ( ( A @ k7_grcat_1 @ ( A @ ( A @ k1_waybel34 ) ) )
= ( A @ k7_grcat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(113,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice5) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel_1) ).
thf(318,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel34) ).
thf(208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(387,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v4_waybel_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel_1) ).
thf(367,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v4_waybel_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(140,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v18_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_waybel_0) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v18_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(198,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v8_waybel_1 ) )
& ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_1) ).
thf(521,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v8_waybel_1 ) )
& ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(130,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_waybel_1) ).
thf(455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_waybel_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(41,axiom,
? [A: $i] : ( A @ l1_orders_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(241,plain,
? [A: $i] : ( A @ l1_orders_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v3_yellow_0 )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(255,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v3_yellow_0 )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(355,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_waybel_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_waybel_1) ).
thf(553,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_waybel_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v3_lattice3 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v5_orders_3 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v4_waybel_1 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v19_waybel_0 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
& ~ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_xboole_0 )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel34) ).
thf(458,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v3_lattice3 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v5_orders_3 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v4_waybel_1 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v21_waybel_0 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v19_waybel_0 ) ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
& ~ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_xboole_0 )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(145,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(162,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ ( C @ v5_waybel_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v18_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_1) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ ( C @ v5_waybel_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v18_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel21) ).
thf(338,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v19_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(470,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(336,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(154,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(75,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( B @ v3_lattice3 )
& ( A @ v3_lattice3 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k2_waybel34 ) ) ) )
<=> ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_waybel34) ).
thf(478,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( B @ v3_lattice3 )
& ( A @ v3_lattice3 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) )
=> ( D
= ( C @ ( B @ ( A @ k2_waybel34 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k2_waybel34 ) ) ) )
=> ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k1_waybel_1 ) ) ) @ v3_waybel_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(383,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(151,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) )
=> ( A @ v3_yellow_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(300,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) )
=> ( A @ v3_yellow_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(27,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(168,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(183,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(273,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(107,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(136,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(400,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ v5_orders_3 ) ) )
& ( B @ v11_quantal1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel10) ).
thf(200,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( B @ v6_waybel_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ v5_orders_3 ) ) )
& ( B @ v11_quantal1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(70,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v8_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v7_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_1) ).
thf(442,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k7_grcat_1 @ v8_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v7_waybel_1 ) )
& ( A @ ( A @ k7_grcat_1 @ v6_waybel_1 ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v23_waybel_0 ) ) )
& ( A @ ( A @ ( A @ k7_grcat_1 @ v5_orders_3 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k7_grcat_1 @ v1_funct_2 ) ) )
& ~ ( A @ k7_grcat_1 @ v1_xboole_0 )
& ( A @ k7_grcat_1 @ v2_funct_1 )
& ( A @ k7_grcat_1 @ v1_funct_1 )
& ( A @ k7_grcat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(78,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v8_waybel_1 ) )
& ( A @ ( B @ v7_waybel_1 ) )
& ( A @ ( B @ v6_waybel_1 ) )
& ( A @ ( A @ ( B @ v22_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v21_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v20_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v19_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v18_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v17_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v5_orders_3 ) ) )
& ( B @ v11_quantal1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel10) ).
thf(501,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v8_waybel_1 ) )
& ( A @ ( B @ v7_waybel_1 ) )
& ( A @ ( B @ v6_waybel_1 ) )
& ( A @ ( A @ ( B @ v22_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v21_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v20_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v19_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v18_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v17_waybel_0 ) ) )
& ( A @ ( A @ ( B @ v5_orders_3 ) ) )
& ( B @ v11_quantal1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ~ ( B @ v1_xboole_0 )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_2) ).
thf(227,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(607,plain,
$false,
inference(e,[status(thm)],[472,125,188,99,365,101,249,555,170,308,120,174,565,492,179,376,485,280,243,265,302,160,561,392,97,329,109,193,134,343,105,360,398,412,430,166,149,423,191,118,259,540,86,113,219,318,208,387,367,103,140,213,198,521,130,455,241,255,355,553,458,145,162,531,127,338,470,336,154,478,383,151,300,168,183,273,107,136,400,200,442,501,111,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT356+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n019.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 21:16:03 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.27 % [INFO] Parsing done (296ms).
% 1.55/1.28 % [INFO] Running in sequential loop mode.
% 2.62/1.67 % [INFO] eprover registered as external prover.
% 2.62/1.67 % [INFO] Scanning for conjecture ...
% 3.03/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 129 axioms. Running axiom selection ...
% 3.38/1.95 % [INFO] Axiom selection finished. Selected 83 axioms (removed 46 axioms).
% 3.81/2.13 % [INFO] Problem is first-order (TPTP FOF).
% 4.05/2.14 % [INFO] Type checking passed.
% 4.05/2.15 % [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 ...
% 12.73/4.20 % External prover 'e' found a proof!
% 12.73/4.20 % [INFO] Killing All external provers ...
% 12.73/4.21 % Time passed: 3663ms (effective reasoning time: 2919ms)
% 12.73/4.21 % 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)>
% 12.73/4.21 % Axioms used in derivation (83): rc2_yellow_0, rc1_funct_1, cc3_waybel_1, t6_boole, cc4_yellow_0, dt_l1_orders_2, fc1_struct_0, redefinition_m2_relset_1, dt_k7_grcat_1, cc1_waybel17, rc4_yellow_9, cc2_finset_1, cc1_waybel21, fc3_waybel_1, fc4_waybel10, dt_k1_waybel34, cc7_waybel_0, fc3_waybel10, rc4_finset_1, cc1_setfam_1, existence_m1_waybel_1, d2_waybel34, t1_subset, rc2_waybel10, fc5_waybel_1, rc1_waybel10, fc4_waybel_1, rc3_waybel_1, cc12_waybel_0, rc3_funct_1, cc1_lattice3, dt_m2_relset_1, cc11_waybel_0, cc14_waybel_0, fc2_waybel34, t5_subset, cc9_waybel_0, existence_m1_relset_1, t4_subset, cc2_waybel_1, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, fc1_waybel34, cc13_waybel_0, rc2_funct_1, cc1_yellow_2, rc3_yellow_9, cc1_waybel10, cc2_funct_1, cc1_relset_1, existence_m1_subset_1, d1_waybel34, rc1_waybel_1, existence_m2_relset_1, fc2_waybel_1, rc2_waybel_1, cc10_waybel_0, cc5_yellow_0, rc3_finset_1, cc6_waybel_0, rc1_finset_1, redefinition_k1_waybel_1, cc1_finset_1, cc4_waybel_1, cc1_yellow_0, t8_boole, rc1_waybel34, rc5_struct_0, t2_subset, cc8_waybel_0, cc2_lattice3, t6_waybel34, existence_l1_struct_0, dt_k1_waybel_1, rc1_setfam_1, rc1_lattice5, dt_k2_waybel34, fc14_finset_1, cc3_yellow_0, cc1_waybel_1, antisymmetry_r2_hidden
% 12.73/4.21 % No. of inferences in proof: 170
% 12.73/4.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3663 ms resp. 2919 ms w/o parsing
% 13.11/4.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.11/4.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------