%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT380+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 : n018.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 07:47:36 AM UTC 2026
% Result : Theorem 129.09s 36.30s
% Output : Refutation 130.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 139
% Syntax : Number of formulae : 702 ( 207 unt; 0 typ; 20 def)
% Number of atoms : 3500 ( 275 equ; 0 cnn)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 11210 ( 844 ~; 521 |;1580 &;7878 @)
% ( 7 <=>; 380 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 85 usr; 19 con; 0-4 aty)
% Number of variables : 1380 ( 7 ^;1291 !; 62 ?;1380 :)
% ( 0 !>; 0 ?*; 0 @-; 20 @+)
% 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(v2_waybel_8_decl,type,
v2_waybel_8: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v17_waybel_0_decl,type,
v17_waybel_0: $i > $i > $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v22_waybel_0_decl,type,
v22_waybel_0: $i > $i > $i > $o ).
thf(k8_relset_1_decl,type,
k8_relset_1: $i > $i > $i > $i > $i ).
thf(k1_waybel34_decl,type,
k1_waybel34: $i > $i > $i > $i ).
thf(k1_waybel_8_decl,type,
k1_waybel_8: $i > $i ).
thf(v4_waybel34_decl,type,
v4_waybel34: $i > $i > $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $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(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k7_relat_1_decl,type,
k7_relat_1: $i > $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g1_orders_2_decl,type,
g1_orders_2: $i > $i > $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v1_orders_2_decl,type,
v1_orders_2: $i > $o ).
thf(u1_orders_2_decl,type,
u1_orders_2: $i > $i ).
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(v5_waybel34_decl,type,
v5_waybel34: $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(v4_yellow_0_decl,type,
v4_yellow_0: $i > $i > $o ).
thf(m1_yellow_0_decl,type,
m1_yellow_0: $i > $i > $o ).
thf(v21_waybel_0_decl,type,
v21_waybel_0: $i > $i > $i > $o ).
thf(r3_orders_2_decl,type,
r3_orders_2: $i > $i > $i > $o ).
thf(v1_waybel_8_decl,type,
v1_waybel_8: $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v5_orders_3_decl,type,
v5_orders_3: $i > $i > $i > $o ).
thf(v6_waybel34_decl,type,
v6_waybel34: $i > $i > $o ).
thf(v6_yellow_0_decl,type,
v6_yellow_0: $i > $i > $o ).
thf(v7_waybel34_decl,type,
v7_waybel34: $i > $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v2_waybel_3_decl,type,
v2_waybel_3: $i > $o ).
thf(v3_waybel_3_decl,type,
v3_waybel_3: $i > $o ).
thf(r1_orders_2_decl,type,
r1_orders_2: $i > $i > $i > $o ).
thf(v1_waybel34_decl,type,
v1_waybel34: $i > $i > $i > $o ).
thf(v5_waybel_1_decl,type,
v5_waybel_1: $i > $i > $i > $o ).
thf(r1_waybel_3_decl,type,
r1_waybel_3: $i > $i > $i > $o ).
thf(v3_waybel34_decl,type,
v3_waybel34: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk27_decl,type,
sk27: $i ).
thf(sk28_decl,type,
sk28: $i ).
thf(sk30_decl,type,
sk30: $i ).
thf(sk33_decl,type,
sk33: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[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 ) )
=> ! [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 ) )
=> ( ( B @ v2_waybel_8 )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) )
=> ( B @ ( A @ ( C @ v22_waybel_0 ) ) ) )
& ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
=> ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[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 @ v2_waybel_8 )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( sk1 @ ( B @ v17_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( sk1 @ k1_waybel_8 @ ( A @ k1_waybel_8 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) )
=> ( A @ ( sk1 @ ( B @ v22_waybel_0 ) ) ) )
& ( ( A @ ( sk1 @ ( B @ v22_waybel_0 ) ) )
=> ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( sk1 @ k1_waybel_8 @ ( A @ k1_waybel_8 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ ( A @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( A @ m2_relset_1 ) ) )
& ( sk2 @ ( sk1 @ ( A @ v17_waybel_0 ) ) )
& ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) )
=> ( sk2 @ ( sk1 @ ( A @ v22_waybel_0 ) ) ) )
& ( ( sk2 @ ( sk1 @ ( A @ v22_waybel_0 ) ) )
=> ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( A @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] : ( A @ l1_orders_2 ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ m2_relset_1 ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_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 @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( @+[A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ v25_waybel_0 )
& ( A @ v24_waybel_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 @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( @+[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 ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
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 ) )
=> ! [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 ) )
=> ( ( B @ v2_waybel_8 )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_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 @ v22_waybel_0 ) ) )
<=> ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_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 ) )
=> ! [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 ) )
=> ( ( B @ v2_waybel_8 )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_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 @ v22_waybel_0 ) ) )
<=> ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(121,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 ) )
=> ! [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 ) )
=> ( ( B @ v2_waybel_8 )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) )
=> ( B @ ( A @ ( C @ v22_waybel_0 ) ) ) )
& ( ( B @ ( A @ ( C @ v22_waybel_0 ) ) )
=> ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(122,plain,
( ( ~ ( sk2 @ ( sk1 @ ( sk3 @ v22_waybel_0 ) ) )
| sk4 )
& ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| sk4 )
& ( ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| sk4 )
& ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
| sk4 )
& ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 )
| sk4 )
& ( ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
| ~ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) )
& ( ~ sk4
| ( sk2 @ ( sk1 @ ( sk3 @ v22_waybel_0 ) ) ) )
& ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ m2_relset_1 ) ) )
& ( sk2 @ ( sk1 @ ( sk3 @ v17_waybel_0 ) ) )
& ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ v1_funct_2 ) ) )
& ( sk3 @ v1_funct_1 )
& ( sk2 @ v2_waybel_8 )
& ( sk2 @ l1_orders_2 )
& ( sk2 @ v3_lattice3 )
& ( sk2 @ v2_lattice3 )
& ( sk2 @ v1_lattice3 )
& ( sk2 @ v4_orders_2 )
& ( sk2 @ v3_orders_2 )
& ( sk2 @ v2_orders_2 )
& ( sk1 @ l1_orders_2 )
& ( sk1 @ v3_lattice3 )
& ( sk1 @ v2_lattice3 )
& ( sk1 @ v1_lattice3 )
& ( sk1 @ v4_orders_2 )
& ( sk1 @ v3_orders_2 )
& ( sk1 @ v2_orders_2 ) ),
inference(cnf,[status(esa)],[121]) ).
thf(138,plain,
sk1 @ v1_lattice3,
inference(cnfConj,[status(thm)],[122]) ).
thf(106,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(720,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(721,plain,
( ( sk33 @ v1_funct_1 )
& ( sk33 @ v1_xboole_0 )
& ( sk33 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[720]) ).
thf(723,plain,
sk33 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[721]) ).
thf(11,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(171,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(172,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A != B ) )
& ( A @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[171]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ( A = B )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 )
| ( A = B ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(241,plain,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(242,plain,
( ( sk12 @ v3_lattice3 )
& ( sk12 @ v2_lattice3 )
& ( sk12 @ v1_lattice3 )
& ( sk12 @ v4_orders_2 )
& ( sk12 @ v3_orders_2 )
& ( sk12 @ v2_orders_2 )
& ( sk12 @ v1_orders_2 )
& ~ ( sk12 @ v3_struct_0 )
& ( sk12 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[241]) ).
thf(251,plain,
sk12 @ v1_lattice3,
inference(cnfConj,[status(thm)],[242]) ).
thf(48,axiom,
? [A: $i] : ( A @ l1_orders_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(332,plain,
? [A: $i] : ( A @ l1_orders_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(333,plain,
sk16 @ l1_orders_2,
inference(cnf,[status(esa)],[332]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(315,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(316,plain,
! [A: $i] :
( ~ ( A @ v3_struct_0 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[315]) ).
thf(829,plain,
! [A: $i] :
( ( ( sk16 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[333,316]) ).
thf(830,plain,
! [A: $i] :
( ( ( sk16 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ v1_lattice3 ) ),
inference(simp,[status(thm)],[829]) ).
thf(831,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_lattice3 ) ),
inference(pattern_uni,[status(thm)],[830:[bind(A,$thf( sk16 ))]]) ).
thf(863,plain,
( ( ( sk16 @ v1_lattice3 )
!= ( sk12 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,831]) ).
thf(864,plain,
( ( ( sk16 @ v1_lattice3 )
!= ( sk12 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[863]) ).
thf(867,plain,
( ( sk16 != sk12 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[864]) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ( A != sk16 )
| ( B != sk12 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,867]) ).
thf(2730,plain,
! [A: $i] :
( ( A != sk12 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2729:[bind(A,$thf( sk16 ))]]) ).
thf(3203,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk12 @ v1_xboole_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2730]) ).
thf(4259,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk12 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[723,3203]) ).
thf(4260,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk12 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4259]) ).
thf(4262,plain,
( ( sk33 != sk12 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4260]) ).
thf(78,axiom,
? [A: $i] :
( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_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 @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(504,plain,
? [A: $i] :
( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_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 @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(505,plain,
( ( sk21 @ v25_waybel_0 )
& ( sk21 @ v24_waybel_0 )
& ( sk21 @ v3_yellow_0 )
& ( sk21 @ v2_yellow_0 )
& ( sk21 @ v1_yellow_0 )
& ( sk21 @ v3_lattice3 )
& ( sk21 @ v2_lattice3 )
& ( sk21 @ v1_lattice3 )
& ( sk21 @ v4_orders_2 )
& ( sk21 @ v3_orders_2 )
& ( sk21 @ v2_orders_2 )
& ( sk21 @ v1_orders_2 )
& ~ ( sk21 @ v3_struct_0 )
& ( sk21 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[504]) ).
thf(518,plain,
sk21 @ v2_yellow_0,
inference(cnfConj,[status(thm)],[505]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel_8) ).
thf(234,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,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(201,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)],[21]) ).
thf(202,plain,
! [A: $i] :
( ( ( A @ sk7 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk7 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk7 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[201]) ).
thf(203,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ sk7 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[202]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(190,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(miniscope,[status(thm)],[189]) ).
thf(191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( D @ ( C @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
| ~ ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ~ ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[191]) ).
thf(4675,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk7 @ m1_subset_1 ) )
!= ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r1_tarski ) )
| ~ $true
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[203,192]) ).
thf(4676,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk7 @ m1_subset_1 ) )
!= ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r1_tarski ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4675]) ).
thf(4677,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ r1_tarski ) )
| ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[4676:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 )),bind(C,$thf( D ))]]) ).
thf(4682,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ r1_tarski ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4677]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(480,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(481,plain,
! [A: $i] :
( ~ ( A @ v3_struct_0 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[480]) ).
thf(249,plain,
sk12 @ l1_orders_2,
inference(cnfConj,[status(thm)],[242]) ).
thf(92,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) ) )
=> ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v6_waybel34 ) )
& ( B @ v1_lattice3 )
& ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_waybel34) ).
thf(628,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) ) )
=> ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v6_waybel34 ) )
& ( B @ v1_lattice3 )
& ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(86,axiom,
? [A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ v25_waybel_0 )
& ( A @ v24_waybel_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 @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_3) ).
thf(573,plain,
? [A: $i] :
( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ v25_waybel_0 )
& ( A @ v24_waybel_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 @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(574,plain,
( ( sk27 @ v3_waybel_3 )
& ( sk27 @ v2_waybel_3 )
& ( sk27 @ v25_waybel_0 )
& ( sk27 @ v24_waybel_0 )
& ( sk27 @ v3_yellow_0 )
& ( sk27 @ v2_yellow_0 )
& ( sk27 @ v1_yellow_0 )
& ( sk27 @ v3_lattice3 )
& ( sk27 @ v2_lattice3 )
& ( sk27 @ v1_lattice3 )
& ( sk27 @ v4_orders_2 )
& ( sk27 @ v3_orders_2 )
& ( sk27 @ v2_orders_2 )
& ( sk27 @ v1_orders_2 )
& ~ ( sk27 @ v3_struct_0 )
& ( sk27 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[573]) ).
thf(582,plain,
~ ( sk27 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[574]) ).
thf(108,axiom,
! [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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v1_waybel34 ) ) )
=> ( A @ ( B @ ( C @ v3_waybel34 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_waybel34) ).
thf(730,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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v1_waybel34 ) ) )
=> ( A @ ( B @ ( C @ v3_waybel34 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(220,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(221,plain,
( ( sk11 @ v1_finset_1 )
& ~ ( sk11 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[220]) ).
thf(222,plain,
~ ( sk11 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[221]) ).
thf(1066,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,222]) ).
thf(1067,plain,
( ( sk33 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1066]) ).
thf(1068,plain,
sk33 != sk11,
inference(simp,[status(thm)],[1067]) ).
thf(42,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ m1_yellow_0 ) )
& ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel_8) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ m1_yellow_0 ) )
& ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(102,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(682,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(683,plain,
( ( sk30 @ v1_funct_1 )
& ( sk30 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[682]) ).
thf(684,plain,
sk30 @ v1_relat_1,
inference(cnfConj,[status(thm)],[683]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(161,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] : ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(miniscope,[status(thm)],[160]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[161]) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ( ( sk30 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[684,162]) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ( ( sk30 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1050]) ).
thf(1052,plain,
! [A: $i] : ( A @ ( sk30 @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1051:[bind(A,$thf( sk30 ))]]) ).
thf(1053,plain,
! [A: $i] : ( A @ ( sk30 @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1052]) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk30 @ k7_relat_1 ) @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( C @ ( B @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1053,162]) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk30 @ k7_relat_1 ) @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( C @ ( B @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1084]) ).
thf(1086,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1085:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk30 @ k7_relat_1 ) )),bind(C,$thf( C ))]]) ).
thf(1087,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1086]) ).
thf(1131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1087,162]) ).
thf(1132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) )),bind(D,$thf( D ))]]) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1133]) ).
thf(3641,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1134,162]) ).
thf(3642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3641]) ).
thf(3643,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3642:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( G @ ( I @ ( K @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(E,$thf( E ))]]) ).
thf(3650,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3643]) ).
thf(3906,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3650,162]) ).
thf(3907,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3906]) ).
thf(3908,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3907:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( H @ ( J @ ( L @ ( N @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(F,$thf( F ))]]) ).
thf(3912,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3908]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(158,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(159,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(cnf,[status(esa)],[158]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnfConj,[status(thm)],[191]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(4906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[159,194]) ).
thf(4907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(simp,[status(thm)],[4906]) ).
thf(4908,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
inference(pattern_uni,[status(thm)],[4907:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(8,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(163,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)],[8]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ v1_relat_1 )
| ~ ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(4927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
| ( D @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4908,164]) ).
thf(4928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
| ( D @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4927]) ).
thf(4929,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4928:[bind(A,$thf( F @ ( E @ k2_zfmisc_1 ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ k2_zfmisc_1 ) ))]]) ).
thf(4948,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4929]) ).
thf(4956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4948,162]) ).
thf(4957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4956]) ).
thf(4958,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4957:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ k2_zfmisc_1 ) ))]]) ).
thf(4961,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4958]) ).
thf(4971,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4961,162]) ).
thf(4972,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4971]) ).
thf(4973,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4972:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ k2_zfmisc_1 ) @ k7_relat_1 ) )),bind(E,$thf( E ))]]) ).
thf(4978,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4973]) ).
thf(5068,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4978,162]) ).
thf(5069,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[5068]) ).
thf(5070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[5069:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( H @ ( J @ ( L @ ( K @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(F,$thf( F ))]]) ).
thf(5077,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[5070]) ).
thf(5094,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5077,162]) ).
thf(5095,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[5094]) ).
thf(5096,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[5095:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( I @ ( K @ ( M @ ( O @ ( N @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(G,$thf( G ))]]) ).
thf(5101,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[5096]) ).
thf(5126,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5101,162]) ).
thf(5127,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[5126]) ).
thf(5128,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[5127:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( R )),bind(G,$thf( J @ ( L @ ( N @ ( P @ ( R @ ( Q @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(H,$thf( H ))]]) ).
thf(5135,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[5128]) ).
thf(5164,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( H @ v1_relat_1 ) )
| ( I @ ( H @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5135,162]) ).
thf(5165,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( H @ v1_relat_1 ) )
| ( I @ ( H @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[5164]) ).
thf(5166,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( H @ ( G @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[5165:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( Q )),bind(E,$thf( S )),bind(F,$thf( T )),bind(G,$thf( U )),bind(H,$thf( K @ ( M @ ( O @ ( Q @ ( S @ ( U @ ( T @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(I,$thf( I ))]]) ).
thf(5173,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( H @ ( G @ k2_zfmisc_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[5166]) ).
thf(247,plain,
~ ( sk12 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[242]) ).
thf(511,plain,
sk21 @ v3_yellow_0,
inference(cnfConj,[status(thm)],[505]) ).
thf(87,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(591,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)],[87]) ).
thf(592,plain,
( ( sk28 @ v3_yellow_0 )
& ( sk28 @ v2_yellow_0 )
& ( sk28 @ v1_yellow_0 )
& ( sk28 @ v3_lattice3 )
& ( sk28 @ v2_lattice3 )
& ( sk28 @ v1_lattice3 )
& ( sk28 @ v4_orders_2 )
& ( sk28 @ v3_orders_2 )
& ( sk28 @ v2_orders_2 )
& ~ ( sk28 @ v3_struct_0 )
& ( sk28 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[591]) ).
thf(597,plain,
sk28 @ v3_lattice3,
inference(cnfConj,[status(thm)],[592]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v6_waybel34 ) )
=> ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v6_yellow_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel34) ).
thf(408,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v6_waybel34 ) )
=> ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v6_yellow_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(10,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(169,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)],[10]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 )
| ~ ( B @ ( A @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(142,plain,
sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(104,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(698,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)],[104]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(153,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_orders_2 ) )
= ( D @ ( C @ g1_orders_2 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_orders_2 ) )
= ( D @ ( C @ g1_orders_2 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B = D )
| ( ( B @ ( A @ g1_orders_2 ) )
!= ( D @ ( C @ g1_orders_2 ) ) )
| ~ ( A @ ( A @ ( B @ m1_relset_1 ) ) ) )
& ( ( A = C )
| ( ( B @ ( A @ g1_orders_2 ) )
!= ( D @ ( C @ g1_orders_2 ) ) )
| ~ ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ g1_orders_2 ) )
!= ( D @ ( C @ g1_orders_2 ) ) )
| ~ ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ m1_relset_1 ) ) )
| ( A = C )
| ( ( B @ ( A @ g1_orders_2 ) )
!= ( D @ ( C @ g1_orders_2 ) ) ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(105,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 @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v4_waybel34 ) ) )
& ( 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_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',rc6_waybel34) ).
thf(709,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 @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v4_waybel34 ) ) )
& ( 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_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)],[105]) ).
thf(40,axiom,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(285,plain,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(286,plain,
( ( sk14 @ v3_lattice3 )
& ( sk14 @ v4_orders_2 )
& ( sk14 @ v3_orders_2 )
& ( sk14 @ v2_orders_2 )
& ( sk14 @ v1_orders_2 )
& ~ ( sk14 @ v3_struct_0 )
& ( sk14 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[285]) ).
thf(288,plain,
sk14 @ v3_orders_2,
inference(cnfConj,[status(thm)],[286]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_waybel_8 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ v24_waybel_0 )
& ( A @ v2_yellow_0 )
& ( 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',cc1_waybel_8) ).
thf(436,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_waybel_8 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ v3_waybel_3 )
& ( A @ v2_waybel_3 )
& ( A @ v24_waybel_0 )
& ( A @ v2_yellow_0 )
& ( 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)],[67]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_orders_2 @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(651,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_orders_2 @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(59,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(389,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)],[59]) ).
thf(724,plain,
sk33 @ v1_funct_1,
inference(cnfConj,[status(thm)],[721]) ).
thf(509,plain,
sk21 @ v1_lattice3,
inference(cnfConj,[status(thm)],[505]) ).
thf(874,plain,
( ( ( sk21 @ v1_lattice3 )
!= ( sk16 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[509,831]) ).
thf(875,plain,
( ( ( sk21 @ v1_lattice3 )
!= ( sk16 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[874]) ).
thf(876,plain,
( ( sk21 != sk16 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[875]) ).
thf(2509,plain,
! [B: $i,A: $i] :
( ( A != sk21 )
| ( B != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,876]) ).
thf(2510,plain,
! [A: $i] :
( ( A != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2509:[bind(A,$thf( sk21 ))]]) ).
thf(3142,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2510]) ).
thf(3974,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[723,3142]) ).
thf(3975,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3974]) ).
thf(3976,plain,
( ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3975]) ).
thf(57,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_waybel_8 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_waybel_8 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_waybel_8 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v24_waybel_0 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_waybel_8) ).
thf(372,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_waybel_8 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_waybel_8 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_waybel_8 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v24_waybel_0 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(587,plain,
sk27 @ v2_yellow_0,
inference(cnfConj,[status(thm)],[574]) ).
thf(125,plain,
sk2 @ v3_lattice3,
inference(cnfConj,[status(thm)],[122]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m1_subset_1 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( B @ v3_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v3_membered ) )
& ( ( B @ v2_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v3_membered ) )
& ( ( B @ v1_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v3_membered ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ v3_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v3_membered ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(722,plain,
sk33 @ v1_relat_1,
inference(cnfConj,[status(thm)],[721]) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ( ( sk33 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,162]) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ( ( sk33 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1057]) ).
thf(1059,plain,
! [A: $i] : ( A @ ( sk33 @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( sk33 ))]]) ).
thf(1060,plain,
! [A: $i] : ( A @ ( sk33 @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1059]) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk33 @ k7_relat_1 ) @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( C @ ( B @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1060,162]) ).
thf(1096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk33 @ k7_relat_1 ) @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( C @ ( B @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1095]) ).
thf(1097,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1096:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk33 @ k7_relat_1 ) )),bind(C,$thf( C ))]]) ).
thf(1098,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1097]) ).
thf(3565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,162]) ).
thf(3566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3565]) ).
thf(3567,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3566:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) )),bind(D,$thf( D ))]]) ).
thf(3574,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3567]) ).
thf(798,plain,
! [A: $i] :
( ( ( sk1 @ v1_lattice3 )
!= ( A @ v1_lattice3 ) )
| ~ ( A @ v3_struct_0 )
| ~ $true
| ~ ( A @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[138,316]) ).
thf(799,plain,
! [A: $i] :
( ( ( sk1 @ v1_lattice3 )
!= ( A @ v1_lattice3 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ l1_orders_2 ) ),
inference(simp,[status(thm)],[798]) ).
thf(800,plain,
( ~ ( sk1 @ v3_struct_0 )
| ~ ( sk1 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[799:[bind(A,$thf( sk1 ))]]) ).
thf(141,plain,
sk1 @ l1_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(816,plain,
( ~ ( sk1 @ v3_struct_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[800,141]) ).
thf(817,plain,
~ ( sk1 @ v3_struct_0 ),
inference(simp,[status(thm)],[816]) ).
thf(4185,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3912,162]) ).
thf(4186,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4185]) ).
thf(4187,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4186:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( I @ ( K @ ( M @ ( O @ ( Q @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(G,$thf( G ))]]) ).
thf(4200,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4187]) ).
thf(4486,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4200,162]) ).
thf(4487,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4486]) ).
thf(4488,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4487:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( J @ ( L @ ( N @ ( P @ ( R @ ( T @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(H,$thf( H ))]]) ).
thf(4492,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk30 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4488]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(151,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(152,plain,
! [A: $i] :
( ( A @ v1_membered )
| ~ ( A @ v2_membered ) ),
inference(cnf,[status(esa)],[151]) ).
thf(289,plain,
sk14 @ v1_orders_2,
inference(cnfConj,[status(thm)],[286]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_waybel_3 )
& ( 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_waybel_3 )
& ( A @ v1_yellow_0 )
& ( 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',cc5_waybel_3) ).
thf(448,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_waybel_3 )
& ( 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_waybel_3 )
& ( A @ v1_yellow_0 )
& ( 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)],[68]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(206,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(207,plain,
! [A: $i] : ( A @ ( A @ sk8 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[206]) ).
thf(1105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
| ( D @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,164]) ).
thf(1106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
| ( D @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1107,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( H @ ( G @ k2_zfmisc_1 ) @ k1_zfmisc_1 )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 ))]]) ).
thf(1121,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ v1_relat_1 ),
inference(simp,[status(thm)],[1107]) ).
thf(3587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1121,162]) ).
thf(3588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3587]) ).
thf(3589,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3588:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 )),bind(D,$thf( D ))]]) ).
thf(3592,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3589]) ).
thf(3746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3592,162]) ).
thf(3747,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3746]) ).
thf(3748,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3747:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( G @ ( K @ ( J @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) )),bind(E,$thf( E ))]]) ).
thf(3751,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3748]) ).
thf(4107,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3751,162]) ).
thf(4108,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4107]) ).
thf(4109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4108:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( H @ ( J @ ( N @ ( M @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) )),bind(F,$thf( F ))]]) ).
thf(4119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4109]) ).
thf(147,plain,
sk3 @ v1_funct_1,
inference(cnfConj,[status(thm)],[122]) ).
thf(144,plain,
( ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
| ~ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(844,plain,
( ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 )
!= ( sk3 @ v1_funct_1 ) )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[147,144]) ).
thf(845,plain,
( ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 )
!= ( sk3 @ v1_funct_1 ) )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) ) ),
inference(simp,[status(thm)],[844]) ).
thf(853,plain,
( ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) ) ),
inference(simp,[status(thm)],[845]) ).
thf(25,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(216,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(146,plain,
sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(878,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
!= ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ v1_funct_2 ) ) ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[142,853]) ).
thf(879,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
!= ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ v1_funct_2 ) ) ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(891,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[879]) ).
thf(893,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[891]) ).
thf(904,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
!= ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ m2_relset_1 ) ) ) )
| ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ $true
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(paramod_ordered,[status(thm)],[146,893]) ).
thf(905,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
!= ( sk2 @ u1_struct_0 @ ( sk1 @ u1_struct_0 @ ( sk3 @ m2_relset_1 ) ) ) )
| ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(909,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(914,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(924,plain,
( ( ( sk1 @ k1_waybel_8 )
!= sk2 )
| ( ( sk2 @ k1_waybel_8 )
!= sk1 )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[914]) ).
thf(14,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(179,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,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(211,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)],[24]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r3_orders_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r3_orders_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(514,plain,
sk21 @ v4_orders_2,
inference(cnfConj,[status(thm)],[505]) ).
thf(602,plain,
~ ( sk28 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[592]) ).
thf(133,plain,
sk2 @ v1_lattice3,
inference(cnfConj,[status(thm)],[122]) ).
thf(861,plain,
( ( ( sk16 @ v1_lattice3 )
!= ( sk2 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[133,831]) ).
thf(862,plain,
( ( ( sk16 @ v1_lattice3 )
!= ( sk2 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[861]) ).
thf(866,plain,
( ( sk16 != sk2 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[862]) ).
thf(60,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(396,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)],[60]) ).
thf(97,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_8) ).
thf(660,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(243,plain,
sk12 @ v3_orders_2,
inference(cnfConj,[status(thm)],[242]) ).
thf(37,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(265,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)],[37]) ).
thf(507,plain,
sk21 @ v25_waybel_0,
inference(cnfConj,[status(thm)],[505]) ).
thf(293,plain,
sk14 @ v3_lattice3,
inference(cnfConj,[status(thm)],[286]) ).
thf(132,plain,
sk1 @ v2_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(774,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(292,plain,
sk14 @ v2_orders_2,
inference(cnfConj,[status(thm)],[286]) ).
thf(248,plain,
sk12 @ v4_orders_2,
inference(cnfConj,[status(thm)],[242]) ).
thf(512,plain,
sk21 @ v1_orders_2,
inference(cnfConj,[status(thm)],[505]) ).
thf(58,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(381,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)],[58]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_waybel_8 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_waybel_8 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_8) ).
thf(366,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_waybel_8 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_waybel_8 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(49,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(334,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(66,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(431,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(432,plain,
( ( sk20 @ v2_funct_1 )
& ( sk20 @ v1_funct_1 )
& ( sk20 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[431]) ).
thf(433,plain,
sk20 @ v1_relat_1,
inference(cnfConj,[status(thm)],[432]) ).
thf(1017,plain,
! [B: $i,A: $i] :
( ( ( sk20 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[433,162]) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ( ( sk20 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1017]) ).
thf(1019,plain,
! [A: $i] : ( A @ ( sk20 @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1018:[bind(A,$thf( sk20 ))]]) ).
thf(1021,plain,
! [A: $i] : ( A @ ( sk20 @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1019]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_8) ).
thf(349,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(137,plain,
sk2 @ v2_waybel_8,
inference(cnfConj,[status(thm)],[122]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(165,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(598,plain,
sk28 @ l1_orders_2,
inference(cnfConj,[status(thm)],[592]) ).
thf(3718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3574,162]) ).
thf(3719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3718]) ).
thf(3720,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3719:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( G @ ( I @ ( K @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(E,$thf( E ))]]) ).
thf(3725,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3720]) ).
thf(3940,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3725,162]) ).
thf(3941,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3940]) ).
thf(3942,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3941:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( H @ ( J @ ( L @ ( N @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(F,$thf( F ))]]) ).
thf(3948,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3942]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(229,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(252,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,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(197,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)],[19]) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( A != sk16 )
| ( B != sk2 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,866]) ).
thf(1646,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1645:[bind(A,$thf( sk16 ))]]) ).
thf(3423,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1646]) ).
thf(3808,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[723,3423]) ).
thf(3809,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3808]) ).
thf(3810,plain,
( ( sk33 != sk2 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3809]) ).
thf(435,plain,
sk20 @ v2_funct_1,
inference(cnfConj,[status(thm)],[432]) ).
thf(98,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(665,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)],[98]) ).
thf(4325,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ( sk33 != sk2 )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3810]) ).
thf(4326,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ( sk33 != sk2 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[4325]) ).
thf(4327,plain,
( ( sk33 != sk16 )
| ( sk33 != sk2 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[4326]) ).
thf(583,plain,
sk27 @ v2_lattice3,
inference(cnfConj,[status(thm)],[574]) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk20 @ k7_relat_1 ) @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( C @ ( B @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1021,162]) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk20 @ k7_relat_1 ) @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( C @ ( B @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1078,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1077:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk20 @ k7_relat_1 ) )),bind(C,$thf( C ))]]) ).
thf(1079,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1078]) ).
thf(593,plain,
sk28 @ v1_lattice3,
inference(cnfConj,[status(thm)],[592]) ).
thf(1025,plain,
( ( ( sk28 @ v1_lattice3 )
!= ( sk16 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,831]) ).
thf(1026,plain,
( ( ( sk28 @ v1_lattice3 )
!= ( sk16 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1027,plain,
( ( sk28 != sk16 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1026]) ).
thf(4396,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4119,162]) ).
thf(4397,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4396]) ).
thf(4398,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4397:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( I @ ( K @ ( M @ ( Q @ ( P @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(G,$thf( G ))]]) ).
thf(4405,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4398]) ).
thf(4726,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4405,162]) ).
thf(4727,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4726]) ).
thf(4728,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4727:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( S )),bind(F,$thf( T )),bind(G,$thf( J @ ( L @ ( N @ ( P @ ( T @ ( S @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(H,$thf( H ))]]) ).
thf(4740,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ sk8 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4728]) ).
thf(114,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(757,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)],[114]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(224,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(317,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( B @ v2_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v3_membered ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(107,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_waybel_8) ).
thf(725,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(16,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(187,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(188,plain,
sk6 @ l1_struct_0,
inference(cnf,[status(esa)],[187]) ).
thf(54,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(356,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)],[54]) ).
thf(77,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(499,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)],[77]) ).
thf(519,plain,
sk21 @ v24_waybel_0,
inference(cnfConj,[status(thm)],[505]) ).
thf(578,plain,
sk27 @ v3_yellow_0,
inference(cnfConj,[status(thm)],[574]) ).
thf(124,plain,
sk2 @ v3_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(931,plain,
! [A: $i] :
( ( ( sk16 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ v2_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[333,481]) ).
thf(932,plain,
! [A: $i] :
( ( ( sk16 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ v2_lattice3 ) ),
inference(simp,[status(thm)],[931]) ).
thf(933,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v2_lattice3 ) ),
inference(pattern_uni,[status(thm)],[932:[bind(A,$thf( sk16 ))]]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( B @ l1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(669,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( B @ l1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(103,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(686,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)],[103]) ).
thf(4225,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3948,162]) ).
thf(4226,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4225]) ).
thf(4227,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4226:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( I @ ( K @ ( M @ ( O @ ( Q @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(G,$thf( G ))]]) ).
thf(4229,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4227]) ).
thf(4532,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4229,162]) ).
thf(4533,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4532]) ).
thf(4534,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4533:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( J @ ( L @ ( N @ ( P @ ( R @ ( T @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(H,$thf( H ))]]) ).
thf(4545,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk33 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4534]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] :
( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_orders_2 )
& ( A @ ( B @ m1_yellow_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_yellow_0) ).
thf(526,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] :
( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_orders_2 )
& ( A @ ( B @ m1_yellow_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(590,plain,
sk27 @ v4_orders_2,
inference(cnfConj,[status(thm)],[574]) ).
thf(83,axiom,
! [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 @ ( A @ k1_waybel_8 @ v7_waybel34 ) )
& ( A @ ( A @ k1_waybel_8 @ v6_waybel34 ) )
& ( A @ k1_waybel_8 @ v1_lattice3 )
& ( A @ ( A @ k1_waybel_8 @ v6_yellow_0 ) )
& ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v1_yellow_0 )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v3_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 )
& ~ ( A @ k1_waybel_8 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_waybel34) ).
thf(547,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 @ ( A @ k1_waybel_8 @ v7_waybel34 ) )
& ( A @ ( A @ k1_waybel_8 @ v6_waybel34 ) )
& ( A @ k1_waybel_8 @ v1_lattice3 )
& ( A @ ( A @ k1_waybel_8 @ v6_yellow_0 ) )
& ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v1_yellow_0 )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v3_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 )
& ~ ( A @ k1_waybel_8 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(622,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(515,plain,
sk21 @ v2_orders_2,
inference(cnfConj,[status(thm)],[505]) ).
thf(129,plain,
( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
| sk4 ),
inference(cnfConj,[status(thm)],[122]) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A @ v1_lattice3 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,138]) ).
thf(1162,plain,
! [A: $i] :
( ( A @ v1_lattice3 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1161:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(5024,plain,
! [A: $i] :
( ( ( sk33 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A @ v1_lattice3 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,1162]) ).
thf(5025,plain,
! [A: $i] :
( ( ( sk33 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A @ v1_lattice3 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[5024]) ).
thf(5026,plain,
( ( sk33 @ v1_lattice3 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[5025:[bind(A,$thf( sk33 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_yellow_0) ).
thf(457,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ v6_yellow_0 ) )
& ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(134,plain,
sk2 @ v2_lattice3,
inference(cnfConj,[status(thm)],[122]) ).
thf(244,plain,
sk12 @ v2_lattice3,
inference(cnfConj,[status(thm)],[242]) ).
thf(205,plain,
! [A: $i] :
( ( A @ sk7 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[202]) ).
thf(508,plain,
sk21 @ v1_yellow_0,
inference(cnfConj,[status(thm)],[505]) ).
thf(586,plain,
sk27 @ l1_orders_2,
inference(cnfConj,[status(thm)],[574]) ).
thf(128,plain,
( ( sk1 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
| sk4 ),
inference(cnfConj,[status(thm)],[122]) ).
thf(51,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(343,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)],[51]) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1079,162]) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( C @ v1_relat_1 ) )
| ( D @ ( C @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1127]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) )),bind(D,$thf( D ))]]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1129]) ).
thf(3613,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1130,162]) ).
thf(3614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( D @ v1_relat_1 ) )
| ( E @ ( D @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3613]) ).
thf(3615,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3614:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( G @ ( I @ ( K @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(E,$thf( E ))]]) ).
thf(3624,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3615]) ).
thf(55,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(360,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)],[55]) ).
thf(63,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(412,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)],[63]) ).
thf(513,plain,
sk21 @ v3_orders_2,
inference(cnfConj,[status(thm)],[505]) ).
thf(148,plain,
sk1 @ v2_lattice3,
inference(cnfConj,[status(thm)],[122]) ).
thf(112,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 @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v21_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_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_waybel34) ).
thf(745,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 @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( B @ ( A @ ( C @ v21_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_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)],[112]) ).
thf(180,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk5 ) @ m1_relset_1 ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(149,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(601,plain,
sk28 @ v3_yellow_0,
inference(cnfConj,[status(thm)],[592]) ).
thf(584,plain,
sk27 @ v1_lattice3,
inference(cnfConj,[status(thm)],[574]) ).
thf(804,plain,
! [A: $i] :
( ( ( sk2 @ v1_lattice3 )
!= ( A @ v1_lattice3 ) )
| ~ ( A @ v3_struct_0 )
| ~ $true
| ~ ( A @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[133,316]) ).
thf(805,plain,
! [A: $i] :
( ( ( sk2 @ v1_lattice3 )
!= ( A @ v1_lattice3 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ l1_orders_2 ) ),
inference(simp,[status(thm)],[804]) ).
thf(806,plain,
( ~ ( sk2 @ v3_struct_0 )
| ~ ( sk2 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[805:[bind(A,$thf( sk2 ))]]) ).
thf(126,plain,
sk2 @ l1_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(818,plain,
( ~ ( sk2 @ v3_struct_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[806,126]) ).
thf(819,plain,
~ ( sk2 @ v3_struct_0 ),
inference(simp,[status(thm)],[818]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(175,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[175]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v24_waybel_0 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel_8) ).
thf(402,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v24_waybel_0 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(109,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 @ v4_waybel34 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_waybel34) ).
thf(732,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 @ v4_waybel34 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(3806,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk2 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3423]) ).
thf(3807,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3806]) ).
thf(3811,plain,
( ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3807]) ).
thf(1099,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( C @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r2_hidden ) )
| ( C @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,170]) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( C @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r2_hidden ) )
| ( C @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1099]) ).
thf(1101,plain,
! [A: $i] :
( ( A @ ( A @ sk8 @ r2_hidden ) )
| ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1100:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(1125,plain,
! [A: $i] :
( ( A @ ( A @ sk8 @ r2_hidden ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1101]) ).
thf(116,axiom,
! [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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( A @ ( B @ ( C @ v3_waybel34 ) ) )
& ( B @ v2_waybel_8 ) )
=> ( A @ ( B @ ( C @ v1_waybel34 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_waybel34) ).
thf(772,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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( A @ ( B @ ( C @ v3_waybel34 ) ) )
& ( B @ v2_waybel_8 ) )
=> ( A @ ( B @ ( C @ v1_waybel34 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] : ( A @ ( B @ m1_yellow_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(743,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] : ( A @ ( B @ m1_yellow_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(577,plain,
sk27 @ v24_waybel_0,
inference(cnfConj,[status(thm)],[574]) ).
thf(36,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(259,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)],[36]) ).
thf(579,plain,
sk27 @ v25_waybel_0,
inference(cnfConj,[status(thm)],[574]) ).
thf(291,plain,
sk14 @ l1_orders_2,
inference(cnfConj,[status(thm)],[286]) ).
thf(43,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(313,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)],[43]) ).
thf(5044,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( sk33 @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,5026]) ).
thf(5045,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( sk33 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[5044]) ).
thf(5047,plain,
( ( sk33 != sk1 )
| ( sk33 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[5045]) ).
thf(5280,plain,
! [A: $i] :
( ( ( sk33 @ v1_lattice3 )
!= ( A @ v1_lattice3 ) )
| ~ ( A @ v3_struct_0 )
| ~ $true
| ~ ( A @ l1_orders_2 )
| ( sk33 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5047,316]) ).
thf(5281,plain,
! [A: $i] :
( ( ( sk33 @ v1_lattice3 )
!= ( A @ v1_lattice3 ) )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ l1_orders_2 )
| ( sk33 != sk1 ) ),
inference(simp,[status(thm)],[5280]) ).
thf(5282,plain,
( ~ ( sk33 @ v3_struct_0 )
| ~ ( sk33 @ l1_orders_2 )
| ( sk33 != sk1 ) ),
inference(pattern_uni,[status(thm)],[5281:[bind(A,$thf( sk33 ))]]) ).
thf(335,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk17 ) @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[334]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_orders_2 )
=> ( A
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(604,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_orders_2 )
=> ( A
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(217,plain,
( ~ ( sk10 @ v3_struct_0 )
& ( sk10 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[216]) ).
thf(219,plain,
~ ( sk10 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[217]) ).
thf(119,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v4_yellow_0 ) ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel34) ).
thf(784,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( ( A @ ( B @ v7_waybel34 ) )
& ( A @ ( B @ v4_yellow_0 ) ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(859,plain,
( ( ( sk16 @ v1_lattice3 )
!= ( sk1 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,831]) ).
thf(860,plain,
( ( ( sk16 @ v1_lattice3 )
!= ( sk1 @ v1_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[859]) ).
thf(865,plain,
( ( sk16 != sk1 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[860]) ).
thf(2737,plain,
! [B: $i,A: $i] :
( ( A != sk16 )
| ( B != sk1 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,865]) ).
thf(2738,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2737:[bind(A,$thf( sk16 ))]]) ).
thf(3206,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2738]) ).
thf(3679,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3206]) ).
thf(3680,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3679]) ).
thf(3683,plain,
( ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3680]) ).
thf(245,plain,
sk12 @ v3_lattice3,
inference(cnfConj,[status(thm)],[242]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_waybel_3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_3) ).
thf(737,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_waybel_3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_waybel_3 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(599,plain,
sk28 @ v2_orders_2,
inference(cnfConj,[status(thm)],[592]) ).
thf(434,plain,
sk20 @ v1_funct_1,
inference(cnfConj,[status(thm)],[432]) ).
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 @ v4_waybel34 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( 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_waybel34) ).
thf(271,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 @ v4_waybel34 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( 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(23,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(208,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(82,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 ) )
=> ( ( A @ v2_waybel_8 )
<=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( D @ ( A @ r3_orders_2 ) ) )
& ( D @ ( B @ ( A @ r3_orders_2 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( D @ r2_hidden ) ) ) )
& ( C @ ( B @ ( A @ r1_waybel_3 ) ) ) ) ) )
& ( A @ v3_waybel_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_waybel_8) ).
thf(535,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] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( D @ ( A @ r3_orders_2 ) ) )
& ( D @ ( B @ ( A @ r3_orders_2 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( D @ r2_hidden ) ) ) )
& ( C @ ( B @ ( A @ r1_waybel_3 ) ) ) ) ) )
& ( A @ v3_waybel_3 ) )
=> ( A @ v2_waybel_8 ) )
& ( ( A @ v2_waybel_8 )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( D @ ( A @ r3_orders_2 ) ) )
& ( D @ ( B @ ( A @ r3_orders_2 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( D @ r2_hidden ) ) ) )
& ( C @ ( B @ ( A @ r1_waybel_3 ) ) ) ) ) )
& ( A @ v3_waybel_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v1_yellow_0 )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v3_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 )
& ~ ( A @ k1_waybel_8 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_waybel34) ).
thf(323,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v1_yellow_0 )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v3_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 )
& ~ ( A @ k1_waybel_8 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_yellow_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_0) ).
thf(520,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v1_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_yellow_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( B @ v1_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v3_membered ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ m1_subset_1 ) )
| ~ ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[197]) ).
thf(594,plain,
sk28 @ v3_orders_2,
inference(cnfConj,[status(thm)],[592]) ).
thf(140,plain,
sk2 @ ( sk1 @ ( sk3 @ v17_waybel_0 ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(212,plain,
! [A: $i] :
( ( ( A @ sk9 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk9 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk9 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ sk9 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(3972,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3142]) ).
thf(3973,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3972]) ).
thf(3977,plain,
( ( sk33 != sk21 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3973]) ).
thf(685,plain,
sk30 @ v1_funct_1,
inference(cnfConj,[status(thm)],[683]) ).
thf(130,plain,
sk1 @ v4_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_1) ).
thf(768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(223,plain,
sk11 @ v1_finset_1,
inference(cnfConj,[status(thm)],[221]) ).
thf(135,plain,
sk2 @ v4_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(28,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(226,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)],[28]) ).
thf(96,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(653,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)],[96]) ).
thf(3872,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3624,162]) ).
thf(3873,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( E @ v1_relat_1 ) )
| ( F @ ( E @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[3872]) ).
thf(3874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[3873:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( H @ ( J @ ( L @ ( N @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(F,$thf( F ))]]) ).
thf(3876,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3874]) ).
thf(922,plain,
( ( ( sk1 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk2 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 )
!= sk1 )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[914]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( B @ v2_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v2_membered ) )
& ( ( B @ v1_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v2_membered ) ) ),
inference(cnf,[status(esa)],[165]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( B @ v1_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v2_membered ) ),
inference(cnfConj,[status(thm)],[166]) ).
thf(72,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 @ v5_waybel34 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel34) ).
thf(473,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 @ v5_waybel34 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(589,plain,
sk27 @ v3_lattice3,
inference(cnfConj,[status(thm)],[574]) ).
thf(123,plain,
( ~ ( sk2 @ ( sk1 @ ( sk3 @ v22_waybel_0 ) ) )
| sk4 ),
inference(cnfConj,[status(thm)],[122]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v3_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_yellow_0) ).
thf(531,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v3_orders_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(76,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(487,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)],[76]) ).
thf(90,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(617,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)],[90]) ).
thf(516,plain,
sk21 @ v3_lattice3,
inference(cnfConj,[status(thm)],[505]) ).
thf(145,plain,
( ~ sk4
| ( sk2 @ ( sk1 @ ( sk3 @ v22_waybel_0 ) ) ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(580,plain,
sk27 @ v1_yellow_0,
inference(cnfConj,[status(thm)],[574]) ).
thf(93,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v4_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_yellow_0) ).
thf(640,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v4_orders_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(150,plain,
! [A: $i] :
( ( A @ v2_membered )
| ~ ( A @ v3_membered ) ),
inference(cnf,[status(esa)],[149]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( 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 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel34) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v1_yellow_0 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v5_orders_3 ) ) )
& ( 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 )
& ( C @ v1_relat_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(118,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ v6_yellow_0 ) )
& ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v3_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel_8) ).
thf(776,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ v6_yellow_0 ) )
& ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v3_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(20,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(199,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)],[20]) ).
thf(13,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(177,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)],[13]) ).
thf(585,plain,
sk27 @ v3_waybel_3,
inference(cnfConj,[status(thm)],[574]) ).
thf(127,plain,
sk1 @ v3_lattice3,
inference(cnfConj,[status(thm)],[122]) ).
thf(576,plain,
sk27 @ v1_orders_2,
inference(cnfConj,[status(thm)],[574]) ).
thf(3695,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(eqfactor_ordered,[status(thm)],[176]) ).
thf(3696,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[3695:[bind(A,$thf( B ))]]) ).
thf(3697,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3696]) ).
thf(50,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 )
& ~ ( A @ k1_waybel_8 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_8) ).
thf(336,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k1_waybel_8 @ v4_yellow_0 ) )
& ( A @ k1_waybel_8 @ v4_orders_2 )
& ( A @ k1_waybel_8 @ v2_orders_2 )
& ( A @ k1_waybel_8 @ v1_orders_2 )
& ~ ( A @ k1_waybel_8 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(600,plain,
sk28 @ v2_lattice3,
inference(cnfConj,[status(thm)],[592]) ).
thf(595,plain,
sk28 @ v2_yellow_0,
inference(cnfConj,[status(thm)],[592]) ).
thf(3681,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[723,3206]) ).
thf(3682,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3681]) ).
thf(3684,plain,
( ( sk33 != sk1 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3682]) ).
thf(143,plain,
sk1 @ v3_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(100,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(671,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)],[100]) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ( A != sk28 )
| ( B != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,1027]) ).
thf(1718,plain,
! [A: $i] :
( ( A != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk28 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1717:[bind(A,$thf( sk28 ))]]) ).
thf(3447,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 )
| ~ ( sk28 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1718]) ).
thf(581,plain,
sk27 @ v3_orders_2,
inference(cnfConj,[status(thm)],[574]) ).
thf(250,plain,
sk12 @ v2_orders_2,
inference(cnfConj,[status(thm)],[242]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_orders_2 ) ) )
<=> ( C @ ( B @ ( A @ r1_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(465,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_orders_2 ) ) )
=> ( C @ ( B @ ( A @ r3_orders_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_orders_2 ) ) )
=> ( C @ ( B @ ( A @ r1_orders_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(230,plain,
~ ? [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[229]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[230]) ).
thf(75,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(482,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)],[75]) ).
thf(218,plain,
sk10 @ l1_struct_0,
inference(cnfConj,[status(thm)],[217]) ).
thf(5052,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ( C @ ( B @ m1_subset_1 ) )
| ~ $true
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1125,196]) ).
thf(5053,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ( C @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[5052]) ).
thf(5054,plain,
! [A: $i] :
( ( A @ ( A @ sk8 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[5053:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(5055,plain,
! [A: $i] :
( ( A @ ( A @ sk8 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[5054]) ).
thf(588,plain,
sk27 @ v2_waybel_3,
inference(cnfConj,[status(thm)],[574]) ).
thf(517,plain,
sk21 @ l1_orders_2,
inference(cnfConj,[status(thm)],[505]) ).
thf(46,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(319,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)],[46]) ).
thf(4672,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk9 @ m1_subset_1 ) )
!= ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r1_tarski ) )
| ~ $true
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[213,192]) ).
thf(4673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk9 @ m1_subset_1 ) )
!= ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r1_tarski ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4672]) ).
thf(4674,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ r1_tarski ) )
| ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[4673:[bind(A,$thf( D )),bind(B,$thf( D @ sk9 )),bind(C,$thf( D ))]]) ).
thf(4681,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ r1_tarski ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4674]) ).
thf(4678,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,192]) ).
thf(4679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[4678]) ).
thf(4680,plain,
! [A: $i] : ( A @ ( A @ k1_zfmisc_1 @ sk8 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[4679:[bind(A,$thf( E @ k1_zfmisc_1 )),bind(B,$thf( E @ k1_zfmisc_1 @ sk8 )),bind(C,$thf( E ))]]) ).
thf(4683,plain,
! [A: $i] : ( A @ ( A @ k1_zfmisc_1 @ sk8 @ r1_tarski ) ),
inference(simp,[status(thm)],[4680]) ).
thf(4040,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3683]) ).
thf(4041,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[4040]) ).
thf(4042,plain,
( ( sk33 != sk1 )
| ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[4041]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ g1_orders_2 ) )
!= ( D @ ( C @ g1_orders_2 ) ) )
| ~ ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ m1_relset_1 ) ) )
| ( B = D )
| ( ( B @ ( A @ g1_orders_2 ) )
!= ( D @ ( C @ g1_orders_2 ) ) ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(139,plain,
sk2 @ v2_orders_2,
inference(cnfConj,[status(thm)],[122]) ).
thf(4257,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk12 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3203]) ).
thf(4258,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk12 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4257]) ).
thf(4261,plain,
( ( sk33 != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk12 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4258]) ).
thf(246,plain,
sk12 @ v1_orders_2,
inference(cnfConj,[status(thm)],[242]) ).
thf(73,axiom,
! [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 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_waybel_3 )
& ( B @ v3_lattice3 )
& ( 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 @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_waybel34 ) ) )
=> ( B @ ( A @ ( C @ v22_waybel_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_waybel34) ).
thf(478,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 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_waybel_3 )
& ( B @ v3_lattice3 )
& ( 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 @ ( A @ ( C @ v17_waybel_0 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_waybel34 ) ) )
=> ( B @ ( A @ ( C @ v22_waybel_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(980,plain,
( ( ( sk27 @ v2_lattice3 )
!= ( sk16 @ v2_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,933]) ).
thf(981,plain,
( ( ( sk27 @ v2_lattice3 )
!= ( sk16 @ v2_lattice3 ) )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[980]) ).
thf(982,plain,
( ( sk27 != sk16 )
| ~ ( sk16 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[981]) ).
thf(2891,plain,
! [B: $i,A: $i] :
( ( A != sk27 )
| ( B != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[174,982]) ).
thf(2892,plain,
! [A: $i] :
( ( A != sk16 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk27 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2891:[bind(A,$thf( sk27 ))]]) ).
thf(3245,plain,
( ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 )
| ~ ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2892]) ).
thf(4566,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[723,3245]) ).
thf(4567,plain,
( ( ( sk33 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4566]) ).
thf(4570,plain,
( ( sk33 != sk27 )
| ~ ( sk16 @ v3_struct_0 )
| ~ ( sk16 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4567]) ).
thf(3996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk7 @ m1_subset_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
| ( D @ v1_relat_1 )
| ~ $true
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[203,164]) ).
thf(3997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ sk7 @ m1_subset_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
| ( D @ v1_relat_1 )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3996]) ).
thf(3998,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ sk7 @ v1_relat_1 )
| ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3997:[bind(A,$thf( G @ ( F @ k2_zfmisc_1 ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ k2_zfmisc_1 ) @ sk7 ))]]) ).
thf(4025,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ sk7 @ v1_relat_1 )
| ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3998]) ).
thf(287,plain,
sk14 @ v4_orders_2,
inference(cnfConj,[status(thm)],[286]) ).
thf(290,plain,
~ ( sk14 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[286]) ).
thf(510,plain,
sk21 @ v2_lattice3,
inference(cnfConj,[status(thm)],[505]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( B @ v2_membered )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v2_membered ) ),
inference(cnfConj,[status(thm)],[166]) ).
thf(120,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_waybel_8) ).
thf(790,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(4145,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3876,162]) ).
thf(4146,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( F @ v1_relat_1 ) )
| ( G @ ( F @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4145]) ).
thf(4147,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4146:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( I @ ( K @ ( M @ ( O @ ( Q @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(G,$thf( G ))]]) ).
thf(4157,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4147]) ).
thf(4440,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4157,162]) ).
thf(4441,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( G @ v1_relat_1 ) )
| ( H @ ( G @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4440]) ).
thf(4442,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4441:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( J @ ( L @ ( N @ ( P @ ( R @ ( T @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(H,$thf( H ))]]) ).
thf(4455,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4442]) ).
thf(603,plain,
sk28 @ v1_yellow_0,
inference(cnfConj,[status(thm)],[592]) ).
thf(85,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(564,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)],[85]) ).
thf(506,plain,
~ ( sk21 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[505]) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ( ( sk33 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ $true
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[723,231]) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( ( sk33 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[1063]) ).
thf(1065,plain,
! [A: $i] :
~ ( sk33 @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[1064:[bind(A,$thf( A )),bind(B,$thf( sk33 ))]]) ).
thf(41,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(294,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)],[41]) ).
thf(136,plain,
( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 )
| sk4 ),
inference(cnfConj,[status(thm)],[122]) ).
thf(575,plain,
sk27 @ v2_orders_2,
inference(cnfConj,[status(thm)],[574]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( B @ ( A @ g1_orders_2 ) @ l1_orders_2 )
& ( B @ ( A @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( B @ ( A @ g1_orders_2 ) @ l1_orders_2 )
& ( B @ ( A @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(596,plain,
sk28 @ v4_orders_2,
inference(cnfConj,[status(thm)],[592]) ).
thf(94,axiom,
! [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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v3_waybel34 ) ) )
<=> ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_waybel34) ).
thf(644,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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v18_waybel_0 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) )
=> ( A @ ( B @ ( C @ v3_waybel34 ) ) ) )
& ( ( A @ ( B @ ( C @ v3_waybel34 ) ) )
=> ( ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( A @ k1_waybel_8 @ ( B @ k1_waybel_8 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
& ( A @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ k1_waybel_8 @ u1_struct_0 @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( B @ v1_finset_1 )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[177]) ).
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(277,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(89,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 @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( 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_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',rc2_waybel34) ).
thf(607,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 @ ( A @ ( C @ v22_waybel_0 ) ) )
& ( 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_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)],[89]) ).
thf(131,plain,
( ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) )
| sk4 ),
inference(cnfConj,[status(thm)],[122]) ).
thf(35,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(254,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)],[35]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v2_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_yellow_0) ).
thf(469,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
=> ( ( A @ ( B @ v4_yellow_0 ) )
& ( B @ v2_orders_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(4917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
!= ( C @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r2_hidden ) )
| ( C @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4908,170]) ).
thf(4918,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
!= ( C @ ( B @ m1_subset_1 ) ) )
| ( C @ ( B @ r2_hidden ) )
| ( C @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4917]) ).
thf(4919,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ r2_hidden ) )
| ( A @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[4918:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ k1_zfmisc_1 ))]]) ).
thf(4949,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ r2_hidden ) )
| ( A @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4919]) ).
thf(215,plain,
! [A: $i] :
( ( A @ sk9 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(84,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_8) ).
thf(560,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(232,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(923,plain,
( ( ( sk1 @ k1_waybel_8 )
!= sk2 )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) )
!= sk3 )
| ~ sk4
| ~ ( sk1 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ ( sk2 @ k1_waybel_8 @ u1_struct_0 @ ( sk3 @ ( sk2 @ ( sk1 @ k1_waybel34 ) ) @ ( sk1 @ u1_struct_0 @ ( sk2 @ u1_struct_0 @ k8_relset_1 ) ) ) @ v4_waybel34 ) ) ) ),
inference(simp,[status(thm)],[914]) ).
thf(4776,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( H @ v1_relat_1 ) )
| ( I @ ( H @ k7_relat_1 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4455,162]) ).
thf(4777,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 )
!= ( H @ v1_relat_1 ) )
| ( I @ ( H @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[4776]) ).
thf(4778,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[4777:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( Q )),bind(E,$thf( S )),bind(F,$thf( U )),bind(G,$thf( W )),bind(H,$thf( K @ ( M @ ( O @ ( Q @ ( S @ ( U @ ( W @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) )),bind(I,$thf( I ))]]) ).
thf(4784,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( sk20 @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ k7_relat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4778]) ).
thf(113,axiom,
! [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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_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 @ v22_waybel_0 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_waybel34 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_waybel34) ).
thf(755,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 ) )
=> ! [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 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_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 @ v22_waybel_0 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k1_waybel34 ) ) @ v1_waybel34 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(101,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(676,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)],[101]) ).
thf(10197,plain,
$false,
inference(e,[status(thm)],[138,4262,518,234,4682,481,249,333,628,582,730,1068,308,3912,5173,247,511,597,408,170,142,698,153,174,185,709,288,436,4948,651,389,724,3976,372,587,125,196,157,504,3574,817,4492,152,289,448,316,5077,4119,853,1087,189,216,924,164,179,591,211,238,5135,353,480,121,514,602,147,866,396,133,660,243,265,507,206,293,5101,132,774,292,248,512,201,381,220,366,334,1021,349,192,137,165,598,160,3948,229,252,197,3810,435,665,4327,583,682,1079,1027,4740,757,285,224,317,156,1121,725,188,356,169,593,499,519,578,3650,141,124,933,669,686,4545,526,590,547,622,515,129,5026,1060,457,134,244,205,508,3592,586,128,343,3624,360,412,513,148,745,573,180,149,601,584,819,176,402,732,3811,1125,772,743,577,259,579,291,4978,3751,313,144,5282,335,181,159,604,187,831,219,784,3683,245,737,599,509,434,271,208,535,323,520,155,198,594,140,213,1162,3977,251,685,130,768,3423,223,135,3142,226,431,241,653,3876,922,167,473,722,4405,589,3206,123,162,531,1134,487,617,516,194,145,580,640,150,414,4200,4961,1098,776,5047,1053,199,177,585,127,576,1130,3697,336,600,175,595,3684,143,876,671,3447,581,250,465,231,482,203,218,3725,5055,588,517,319,4681,4683,158,4042,186,171,139,4261,246,207,478,684,4570,4025,287,290,914,433,510,151,315,168,146,790,867,865,3203,4455,603,564,506,195,4157,1065,720,294,126,136,332,575,427,596,644,163,982,178,277,607,3245,723,131,4229,254,469,4949,215,560,222,232,923,4784,4908,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT380+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
% 0.14/0.41 % Computer : n018.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 21:39:05 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.28 % [INFO] Parsing done (301ms).
% 1.54/1.29 % [INFO] Running in sequential loop mode.
% 2.58/1.67 % [INFO] eprover registered as external prover.
% 2.58/1.68 % [INFO] Scanning for conjecture ...
% 3.03/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 137 axioms. Running axiom selection ...
% 3.33/2.00 % [INFO] Axiom selection finished. Selected 118 axioms (removed 19 axioms).
% 4.23/2.17 % [INFO] Problem is first-order (TPTP FOF).
% 4.23/2.19 % [INFO] Type checking passed.
% 4.23/2.19 % [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 ...
% 128.58/36.29 % External prover 'e' found a proof!
% 128.58/36.30 % [INFO] Killing All external provers ...
% 128.58/36.30 % Time passed: 35744ms (effective reasoning time: 35000ms)
% 128.58/36.30 % 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)>
% 129.09/36.30 % Axioms used in derivation (118): redefinition_m2_relset_1, t61_waybel34, redefinition_k8_relset_1, dt_k7_relat_1, rc6_waybel34, rc4_yellow_9, cc2_finset_1, cc1_waybel21, rc3_waybel34, cc1_waybel17, dt_k1_waybel34, rc4_finset_1, cc7_waybel_0, fc10_waybel_8, t7_waybel_8, fc4_funct_1, t1_subset, dt_k8_relset_1, rc2_yellow_0, fc1_waybel_8, rc1_waybel10, t25_waybel34, cc2_waybel_8, cc2_waybel34, cc12_waybel_0, rc3_funct_1, cc4_waybel_3, 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, t70_waybel34, fc8_waybel_8, fc6_waybel_8, rc1_lattice3, cc6_waybel34, rc2_lattice3, t6_boole, redefinition_r3_orders_2, cc7_waybel34, t5_subset, cc9_waybel_0, existence_m1_relset_1, fc7_waybel_8, t4_subset, fc9_waybel_8, cc2_waybel_1, t60_waybel34, fc15_waybel34, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, fc1_waybel34, reflexivity_r3_orders_2, cc12_yellow_0, cc13_waybel_0, dt_g1_orders_2, rc2_funct_1, cc4_membered, cc1_yellow_2, fc3_waybel_8, rc3_yellow_9, dt_k1_waybel_8, cc1_waybel34, cc6_yellow_0, cc18_membered, abstractness_v1_orders_2, cc4_yellow_0, cc2_funct_1, rc4_waybel34, t24_waybel34, t3_subset, cc1_relset_1, existence_m1_subset_1, rc2_waybel_3, existence_m2_relset_1, dt_l1_orders_2, fc14_waybel34, free_g1_orders_2, cc5_waybel_3, fc1_struct_0, cc7_yellow_0, rc4_yellow_0, reflexivity_r1_tarski, cc17_membered, cc4_waybel34, cc10_waybel_0, existence_m1_yellow_0, rc3_finset_1, cc6_waybel_0, fc11_waybel_8, dt_m1_yellow_0, cc5_yellow_0, rc1_finset_1, fc4_waybel_8, cc1_finset_1, cc1_waybel_8, cc1_yellow_0, t8_boole, rc5_struct_0, t2_subset, cc2_lattice3, cc5_waybel34, cc3_membered, rc2_waybel34, existence_l1_struct_0, cc8_yellow_0, fc14_finset_1, cc16_membered, rc1_lattice5, cc3_yellow_0, fc5_waybel_8, antisymmetry_r2_hidden
% 129.09/36.30 % No. of inferences in proof: 682
% 129.09/36.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 35744 ms resp. 35000 ms w/o parsing
% 130.40/36.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 130.40/36.62 % [INFO] Killing All external provers ...
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