%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT374+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 : n016.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 07:47:34 AM UTC 2026
% Result : Theorem 101.25s 30.45s
% Output : Refutation 97.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 156
% Syntax : Number of formulae : 1858 ( 220 unt; 0 typ; 27 def)
% Number of atoms : 8438 (1149 equ; 0 cnn)
% Maximal formula atoms : 143 ( 4 avg)
% Number of connectives : 18689 (3410 ~;3675 |;1191 &;10048 @)
% ( 9 <=>; 356 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 107 usr; 23 con; 0-4 aty)
% Number of variables : 1447 ( 12 ^;1348 !; 60 ?;1447 :)
% ( 0 !>; 0 ?*; 0 @-; 27 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v2_setfam_1_decl,type,
v2_setfam_1: $i > $o ).
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(l1_orders_2_decl,type,
l1_orders_2: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k9_waybel34_decl,type,
k9_waybel34: $i > $i ).
thf(v1_orders_2_decl,type,
v1_orders_2: $i > $o ).
thf(v3_lattice3_decl,type,
v3_lattice3: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(l1_altcat_1_decl,type,
l1_altcat_1: $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k3_zfmisc_1_decl,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(r2_altcat_2_decl,type,
r2_altcat_2: $i > $i > $i > $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v2_altcat_1_decl,type,
v2_altcat_1: $i > $o ).
thf(v11_altcat_1_decl,type,
v11_altcat_1: $i > $o ).
thf(v12_altcat_1_decl,type,
v12_altcat_1: $i > $o ).
thf(v2_yellow18_decl,type,
v2_yellow18: $i > $o ).
thf(l2_altcat_1_decl,type,
l2_altcat_1: $i > $o ).
thf(m1_altcat_2_decl,type,
m1_altcat_2: $i > $i > $o ).
thf(v3_altcat_2_decl,type,
v3_altcat_2: $i > $i > $o ).
thf(v1_altcat_2_decl,type,
v1_altcat_2: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(m3_pboole_decl,type,
m3_pboole: $i > $i > $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(g1_orders_2_decl,type,
g1_orders_2: $i > $i > $i ).
thf(k5_waybel34_decl,type,
k5_waybel34: $i > $i ).
thf(v6_altcat_1_decl,type,
v6_altcat_1: $i > $o ).
thf(v2_yellow21_decl,type,
v2_yellow21: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k3_altcat_1_decl,type,
k3_altcat_1: $i > $i > $i > $i ).
thf(k2_altcat_1_decl,type,
k2_altcat_1: $i > $i > $i ).
thf(g2_altcat_1_decl,type,
g2_altcat_1: $i > $i > $i > $i ).
thf(r1_altcat_2_decl,type,
r1_altcat_2: $i > $i > $o ).
thf(v9_altcat_1_decl,type,
v9_altcat_1: $i > $o ).
thf(v3_yellow18_decl,type,
v3_yellow18: $i > $o ).
thf(v4_yellow18_decl,type,
v4_yellow18: $i > $o ).
thf(v1_yellow21_decl,type,
v1_yellow21: $i > $o ).
thf(v3_yellow21_decl,type,
v3_yellow21: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k1_yellow21_decl,type,
k1_yellow21: $i > $i ).
thf(u1_orders_2_decl,type,
u1_orders_2: $i > $i ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_waybel34_decl,type,
k2_waybel34: $i > $i > $i > $i ).
thf(u1_altcat_1_decl,type,
u1_altcat_1: $i > $i ).
thf(k3_yellow21_decl,type,
k3_yellow21: $i > $i > $i ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(v4_ordinal2_decl,type,
v4_ordinal2: $i > $o ).
thf(v1_xreal_0_decl,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_decl,type,
v1_rat_1: $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
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(u2_altcat_1_decl,type,
u2_altcat_1: $i > $i ).
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(k1_altcat_1_decl,type,
k1_altcat_1: $i > $i > $i > $i ).
thf(k5_yellow21_decl,type,
k5_yellow21: $i > $i > $i > $i > $i ).
thf(v22_waybel_0_decl,type,
v22_waybel_0: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk20_decl,type,
sk20: $i > $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk25_decl,type,
sk25: $i ).
thf(sk26_decl,type,
sk26: $i ).
thf(sk29_decl,type,
sk29: $i ).
thf(sk30_decl,type,
sk30: $i > $i ).
thf(sk31_decl,type,
sk31: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ( A @ v2_setfam_1 )
=> ! [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 @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) )
=> ( A @ k9_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
& ( ( A @ k9_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( ( ( sk1 @ ( A @ u1_struct_0 @ r2_hidden ) )
& ( A @ v3_lattice3 )
& ( A @ v1_orders_2 ) )
=> ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
& ( ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( sk1 @ ( A @ u1_struct_0 @ r2_hidden ) )
& ( A @ v3_lattice3 )
& ( A @ v1_orders_2 ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ m2_relset_1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] : ( A @ ( B @ ( C @ ( D @ m3_pboole ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] : ( A @ l2_altcat_1 ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
( ( A @ v3_yellow21 )
& ( A @ v2_yellow21 )
& ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v6_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_pboole ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_altcat_2 ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] : ( A @ l1_altcat_1 ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[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(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( @+[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(sk25_def,definition,
( sk25
= ( @+[A: $i] : ( A @ l1_orders_2 ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( @+[A: $i] :
~ ( A @ v2_setfam_1 ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( @+[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(sk30_def,definition,
( sk30
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( @+[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(23,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k5_waybel34 @ l2_altcat_1 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_waybel34) ).
thf(221,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k5_waybel34 @ l2_altcat_1 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(222,plain,
! [A: $i] :
( ( ( A @ k5_waybel34 @ l2_altcat_1 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k5_waybel34 @ v2_yellow21 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k5_waybel34 @ v12_altcat_1 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k5_waybel34 @ v11_altcat_1 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k5_waybel34 @ v6_altcat_1 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k5_waybel34 @ v2_altcat_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ k5_waybel34 @ v3_struct_0 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(224,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ l2_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ l1_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_altcat_1) ).
thf(232,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ l1_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(233,plain,
! [A: $i] :
( ( A @ l1_altcat_1 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[232]) ).
thf(3358,plain,
! [B: $i,A: $i] :
( ( ( A @ k5_waybel34 @ l2_altcat_1 )
!= ( B @ l2_altcat_1 ) )
| ( B @ l1_altcat_1 )
| ~ $true
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[224,233]) ).
thf(3359,plain,
! [B: $i,A: $i] :
( ( ( A @ k5_waybel34 @ l2_altcat_1 )
!= ( B @ l2_altcat_1 ) )
| ( B @ l1_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3358]) ).
thf(3360,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ l1_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3359:[bind(A,$thf( C )),bind(B,$thf( C @ k5_waybel34 ))]]) ).
thf(3367,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ l1_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3360]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(148,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(149,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [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 @ k9_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
<=> ( ( A @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_waybel34) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [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 @ k9_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
<=> ( ( A @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(131,plain,
~ ! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [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 @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) )
=> ( A @ k9_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
& ( ( A @ k9_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(132,plain,
( ( ~ ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| sk3 )
& ( ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3 )
& ( ( sk2 @ v3_lattice3 )
| sk3 )
& ( ( sk2 @ v1_orders_2 )
| sk3 )
& ( ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v3_lattice3 )
| ~ ( sk2 @ v1_orders_2 ) )
& ( ~ sk3
| ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) ) )
& ( sk2 @ l1_orders_2 )
& ( sk2 @ v2_lattice3 )
& ( sk2 @ v1_lattice3 )
& ( sk2 @ v4_orders_2 )
& ( sk2 @ v3_orders_2 )
& ( sk2 @ v2_orders_2 )
& ~ ( sk1 @ v2_setfam_1 ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
sk2 @ v2_orders_2,
inference(cnfConj,[status(thm)],[132]) ).
thf(868,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,133]) ).
thf(869,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[868:[bind(A,$thf( sk2 ))]]) ).
thf(6581,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,869]) ).
thf(6582,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6581]) ).
thf(6583,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6582:[bind(A,$thf( sk2 ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_altcat_1) ).
thf(146,plain,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(147,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnf,[status(esa)],[146]) ).
thf(7302,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6583,147]) ).
thf(7303,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[7302]) ).
thf(7304,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(pattern_uni,[status(thm)],[7303:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(15,axiom,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(188,plain,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(189,plain,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[188]) ).
thf(194,plain,
k1_xboole_0 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[189]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(209,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(210,plain,
( ( sk9 @ v1_finset_1 )
& ~ ( sk9 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
~ ( sk9 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[210]) ).
thf(807,plain,
( ( ( sk9 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,211]) ).
thf(808,plain,
( ( sk9 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[807]) ).
thf(809,plain,
sk9 != k1_xboole_0,
inference(simp,[status(thm)],[808]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ v3_yellow21 )
& ( A @ v2_yellow21 )
& ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v6_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow21) ).
thf(247,plain,
? [A: $i] :
( ( A @ v3_yellow21 )
& ( A @ v2_yellow21 )
& ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v6_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(248,plain,
( ( sk13 @ v3_yellow21 )
& ( sk13 @ v2_yellow21 )
& ( sk13 @ v1_yellow21 )
& ( sk13 @ v4_yellow18 )
& ( sk13 @ v3_yellow18 )
& ( sk13 @ v2_yellow18 )
& ( sk13 @ v1_altcat_2 )
& ( sk13 @ v12_altcat_1 )
& ( sk13 @ v11_altcat_1 )
& ( sk13 @ v9_altcat_1 )
& ( sk13 @ v6_altcat_1 )
& ( sk13 @ v2_altcat_1 )
& ~ ( sk13 @ v3_struct_0 )
& ( sk13 @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[247]) ).
thf(260,plain,
sk13 @ l2_altcat_1,
inference(cnfConj,[status(thm)],[248]) ).
thf(987,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,260]) ).
thf(988,plain,
( ( k1_xboole_0 @ l2_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[987:[bind(A,$thf( sk13 ))]]) ).
thf(3951,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,988]) ).
thf(3952,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[3951]) ).
thf(3962,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[3952]) ).
thf(106,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(623,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)],[106]) ).
thf(624,plain,
( ( sk29 @ v25_waybel_0 )
& ( sk29 @ v24_waybel_0 )
& ( sk29 @ v3_yellow_0 )
& ( sk29 @ v2_yellow_0 )
& ( sk29 @ v1_yellow_0 )
& ( sk29 @ v3_lattice3 )
& ( sk29 @ v2_lattice3 )
& ( sk29 @ v1_lattice3 )
& ( sk29 @ v4_orders_2 )
& ( sk29 @ v3_orders_2 )
& ( sk29 @ v2_orders_2 )
& ( sk29 @ v1_orders_2 )
& ~ ( sk29 @ v3_struct_0 )
& ( sk29 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[623]) ).
thf(629,plain,
sk29 @ v1_lattice3,
inference(cnfConj,[status(thm)],[624]) ).
thf(262,plain,
sk13 @ v2_altcat_1,
inference(cnfConj,[status(thm)],[248]) ).
thf(1011,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v2_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,262]) ).
thf(1012,plain,
( ( k1_xboole_0 @ v2_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1011:[bind(A,$thf( sk13 ))]]) ).
thf(4087,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1012]) ).
thf(4088,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_altcat_1 ) ),
inference(simp,[status(thm)],[4087]) ).
thf(4101,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_altcat_1 ) ),
inference(simp,[status(thm)],[4088]) ).
thf(631,plain,
~ ( sk29 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[624]) ).
thf(939,plain,
! [A: $i] :
( ( A != sk29 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,631]) ).
thf(940,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[939:[bind(A,$thf( sk29 ))]]) ).
thf(2021,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,940]) ).
thf(2022,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2021]) ).
thf(2031,plain,
( ( sk29 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2022]) ).
thf(80,axiom,
? [A: $i] : ( A @ l1_orders_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(501,plain,
? [A: $i] : ( A @ l1_orders_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(502,plain,
sk25 @ l1_orders_2,
inference(cnf,[status(esa)],[501]) ).
thf(1994,plain,
! [A: $i] :
( ( A != sk25 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,502]) ).
thf(1995,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk25 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( sk25 ))]]) ).
thf(84,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(518,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)],[84]) ).
thf(26,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(234,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(636,plain,
sk29 @ v2_yellow_0,
inference(cnfConj,[status(thm)],[624]) ).
thf(2289,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v2_yellow_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,636]) ).
thf(2290,plain,
( ( k1_xboole_0 @ v2_yellow_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2289:[bind(A,$thf( sk29 ))]]) ).
thf(6688,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2290]) ).
thf(6689,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6688]) ).
thf(6690,plain,
( ( k1_xboole_0 @ v2_yellow_0 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6689:[bind(A,$thf( sk29 ))]]) ).
thf(92,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(555,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)],[92]) ).
thf(111,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(656,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)],[111]) ).
thf(657,plain,
( ( sk31 @ v3_yellow_0 )
& ( sk31 @ v2_yellow_0 )
& ( sk31 @ v1_yellow_0 )
& ( sk31 @ v3_lattice3 )
& ( sk31 @ v2_lattice3 )
& ( sk31 @ v1_lattice3 )
& ( sk31 @ v4_orders_2 )
& ( sk31 @ v3_orders_2 )
& ( sk31 @ v2_orders_2 )
& ~ ( sk31 @ v3_struct_0 )
& ( sk31 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[656]) ).
thf(666,plain,
sk31 @ v3_yellow_0,
inference(cnfConj,[status(thm)],[657]) ).
thf(57,axiom,
? [A: $i] : ( A @ l1_altcat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_altcat_1) ).
thf(403,plain,
? [A: $i] : ( A @ l1_altcat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(404,plain,
sk19 @ l1_altcat_1,
inference(cnf,[status(esa)],[403]) ).
thf(1109,plain,
! [A: $i] :
( ( A != sk19 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,404]) ).
thf(1110,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk19 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1109:[bind(A,$thf( sk19 ))]]) ).
thf(61,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(422,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)],[61]) ).
thf(423,plain,
! [A: $i] :
( ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[422]) ).
thf(69,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(453,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)],[69]) ).
thf(454,plain,
( ( sk23 @ v3_lattice3 )
& ( sk23 @ v4_orders_2 )
& ( sk23 @ v3_orders_2 )
& ( sk23 @ v2_orders_2 )
& ( sk23 @ v1_orders_2 )
& ~ ( sk23 @ v3_struct_0 )
& ( sk23 @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[453]) ).
thf(461,plain,
~ ( sk23 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[454]) ).
thf(21807,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk23 @ v3_struct_0 ) )
| ~ $true
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[423,461]) ).
thf(21808,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk23 @ v3_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[21807]) ).
thf(21809,plain,
( ~ ( sk23 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk23 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[21808:[bind(A,$thf( sk23 ))]]) ).
thf(460,plain,
sk23 @ l1_orders_2,
inference(cnfConj,[status(thm)],[454]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(429,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(430,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l1_orders_2 ) ),
inference(cnf,[status(esa)],[429]) ).
thf(25558,plain,
! [A: $i] :
( ( ( sk23 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[460,430]) ).
thf(25559,plain,
! [A: $i] :
( ( ( sk23 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25558]) ).
thf(25560,plain,
sk23 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25559:[bind(A,$thf( sk23 ))]]) ).
thf(25609,plain,
( ~ ( sk23 @ u1_struct_0 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[21809,25560]) ).
thf(25610,plain,
~ ( sk23 @ u1_struct_0 @ v1_xboole_0 ),
inference(simp,[status(thm)],[25609]) ).
thf(25689,plain,
( ( ( sk23 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,25610]) ).
thf(25690,plain,
( ( sk23 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[25689]) ).
thf(25695,plain,
( ( sk23 @ u1_struct_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[25690]) ).
thf(108,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(641,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)],[108]) ).
thf(642,plain,
! [A: $i] :
( ( ( A @ sk30 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk30 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk30 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[641]) ).
thf(645,plain,
! [A: $i] :
( ( A @ sk30 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[642]) ).
thf(49,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v2_yellow21 )
& ( B @ v1_yellow21 )
& ( B @ v4_yellow18 )
& ( B @ v3_yellow18 )
& ( B @ v2_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v9_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_yellow21) ).
thf(363,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v2_yellow21 )
& ( B @ v1_yellow21 )
& ( B @ v4_yellow18 )
& ( B @ v3_yellow18 )
& ( B @ v2_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v9_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( ( B @ v2_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v4_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v3_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( A @ ( B @ v3_altcat_2 ) )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v9_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( B @ v2_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(138,plain,
sk2 @ v2_lattice3,
inference(cnfConj,[status(thm)],[132]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(347,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(60,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(411,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)],[60]) ).
thf(412,plain,
( ( 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)],[411]) ).
thf(417,plain,
sk21 @ v3_orders_2,
inference(cnfConj,[status(thm)],[412]) ).
thf(1728,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,417]) ).
thf(1729,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1728:[bind(A,$thf( sk21 ))]]) ).
thf(249,plain,
sk13 @ v1_yellow21,
inference(cnfConj,[status(thm)],[248]) ).
thf(42,axiom,
! [A: $i] : ( A @ k1_yellow21 @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow21) ).
thf(332,plain,
! [A: $i] : ( A @ k1_yellow21 @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(333,plain,
! [A: $i] : ( A @ k1_yellow21 @ l1_struct_0 ),
inference(cnf,[status(esa)],[332]) ).
thf(628,plain,
sk29 @ v3_lattice3,
inference(cnfConj,[status(thm)],[624]) ).
thf(457,plain,
sk23 @ v1_orders_2,
inference(cnfConj,[status(thm)],[454]) ).
thf(456,plain,
sk23 @ v3_lattice3,
inference(cnfConj,[status(thm)],[454]) ).
thf(135,plain,
( ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v3_lattice3 )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(1862,plain,
( ( ( sk23 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true
| ~ ( sk2 @ v1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[456,135]) ).
thf(1863,plain,
( ( ( sk23 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[1862]) ).
thf(1866,plain,
( ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[1863]) ).
thf(9998,plain,
( ( ( sk23 @ v1_orders_2 )
!= ( sk2 @ v1_orders_2 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,1866]) ).
thf(9999,plain,
( ( ( sk23 @ v1_orders_2 )
!= ( sk2 @ v1_orders_2 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9998]) ).
thf(10022,plain,
( ( sk23 != sk2 )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9999]) ).
thf(10025,plain,
( ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10022]) ).
thf(10196,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10025]) ).
thf(10197,plain,
( ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10196:[bind(A,$thf( sk2 ))]]) ).
thf(12972,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10197]) ).
thf(12973,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12972]) ).
thf(12986,plain,
( ( sk2 != k1_xboole_0 )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12973]) ).
thf(16896,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk2 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,12986]) ).
thf(16897,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16896]) ).
thf(16898,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16897:[bind(A,$thf( sk23 ))]]) ).
thf(638,plain,
sk29 @ v1_orders_2,
inference(cnfConj,[status(thm)],[624]) ).
thf(2308,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,638]) ).
thf(2309,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2308:[bind(A,$thf( sk29 ))]]) ).
thf(24,axiom,
? [A: $i] : ( A @ l2_altcat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_altcat_1) ).
thf(230,plain,
? [A: $i] : ( A @ l2_altcat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(231,plain,
sk11 @ l2_altcat_1,
inference(cnf,[status(esa)],[230]) ).
thf(915,plain,
! [A: $i] :
( ( A != sk11 )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,231]) ).
thf(916,plain,
( ( k1_xboole_0 @ l2_altcat_1 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[915:[bind(A,$thf( sk11 ))]]) ).
thf(3355,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[916,233]) ).
thf(3356,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3355]) ).
thf(3357,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3356:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(7438,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,3357]) ).
thf(7439,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7438]) ).
thf(7440,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ( sk11 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7439:[bind(A,$thf( sk11 ))]]) ).
thf(15545,plain,
( ~ $true
| ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( k1_xboole_0 @ l1_altcat_1 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(eqfactor_ordered,[status(thm)],[7440]) ).
thf(15547,plain,
( ( ( sk11 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15545]) ).
thf(139,plain,
sk2 @ v3_orders_2,
inference(cnfConj,[status(thm)],[132]) ).
thf(919,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,139]) ).
thf(920,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[919:[bind(A,$thf( sk2 ))]]) ).
thf(6541,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,920]) ).
thf(6542,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6541]) ).
thf(6543,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6542:[bind(A,$thf( sk2 ))]]) ).
thf(6998,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6543]) ).
thf(6999,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6998:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(16080,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6999]) ).
thf(16081,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[16080]) ).
thf(16086,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ v3_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[16081]) ).
thf(116,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(683,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)],[116]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v3_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_yellow21 )
& ( B @ v2_yellow21 )
& ( B @ v1_yellow21 )
& ( B @ v4_yellow18 )
& ( B @ v3_yellow18 )
& ( B @ v2_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v9_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_yellow21) ).
thf(274,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v3_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_yellow21 )
& ( B @ v2_yellow21 )
& ( B @ v1_yellow21 )
& ( B @ v4_yellow18 )
& ( B @ v3_yellow18 )
& ( B @ v2_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v9_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( ( B @ v3_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v4_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v3_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( A @ ( B @ v3_altcat_2 ) )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v9_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( B @ v4_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(88,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(535,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(536,plain,
~ ! [A: $i] : ( A @ v2_setfam_1 ),
inference(miniscope,[status(thm)],[535]) ).
thf(537,plain,
~ ( sk26 @ v2_setfam_1 ),
inference(cnf,[status(esa)],[536]) ).
thf(884,plain,
! [A: $i] :
( ( A != sk26 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,537]) ).
thf(885,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( sk26 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[884:[bind(A,$thf( sk26 ))]]) ).
thf(6493,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk26 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,885]) ).
thf(6494,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk26 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6493]) ).
thf(6495,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( sk26 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6494:[bind(A,$thf( sk26 ))]]) ).
thf(860,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,138]) ).
thf(861,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( sk2 ))]]) ).
thf(6487,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,861]) ).
thf(6488,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6487]) ).
thf(6489,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6488:[bind(A,$thf( sk2 ))]]) ).
thf(6743,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6489]) ).
thf(6744,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6743:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(421,plain,
sk21 @ v4_orders_2,
inference(cnfConj,[status(thm)],[412]) ).
thf(1807,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,421]) ).
thf(1808,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1807:[bind(A,$thf( sk21 ))]]) ).
thf(1864,plain,
! [A: $i] :
( ( A != sk23 )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,456]) ).
thf(1865,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1864:[bind(A,$thf( sk23 ))]]) ).
thf(6617,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1865]) ).
thf(6618,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6617]) ).
thf(6619,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6618:[bind(A,$thf( sk23 ))]]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ l2_altcat_1 )
& ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ v6_altcat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_altcat_1) ).
thf(306,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ l2_altcat_1 )
& ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ v6_altcat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ l2_altcat_1 )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
& ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ v6_altcat_1 )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ) ),
inference(cnf,[status(esa)],[306]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ v6_altcat_1 )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[307]) ).
thf(2138,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,628]) ).
thf(2139,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2138:[bind(A,$thf( sk29 ))]]) ).
thf(6641,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2139]) ).
thf(6642,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6641]) ).
thf(6643,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6642:[bind(A,$thf( sk29 ))]]) ).
thf(13422,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6643,147]) ).
thf(13423,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[13422]) ).
thf(13424,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(pattern_uni,[status(thm)],[13423:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(51,axiom,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(379,plain,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(419,plain,
sk21 @ v1_lattice3,
inference(cnfConj,[status(thm)],[412]) ).
thf(1742,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,419]) ).
thf(1743,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1742:[bind(A,$thf( sk21 ))]]) ).
thf(4610,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1743]) ).
thf(4611,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[4610]) ).
thf(4614,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[4611]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v3_yellow18 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow21) ).
thf(265,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v3_yellow18 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v3_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( ( B @ v3_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( A @ ( B @ v3_altcat_2 ) )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[265]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[266]) ).
thf(3270,plain,
( ( ( sk11 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,916]) ).
thf(3271,plain,
( ( ( sk11 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[3270]) ).
thf(3281,plain,
( ( sk11 != k1_xboole_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[3271]) ).
thf(7206,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true
| ( sk11 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[3281,233]) ).
thf(7207,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ( sk11 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[7206]) ).
thf(7208,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ( sk11 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7207:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(6478,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk19 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1110]) ).
thf(6479,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk19 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6478]) ).
thf(6480,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ( sk19 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6479:[bind(A,$thf( sk19 ))]]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_functor0) ).
thf(183,plain,
? [A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(184,plain,
( ( sk5 @ v1_altcat_2 )
& ~ ( sk5 @ v3_struct_0 )
& ( sk5 @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[183]) ).
thf(185,plain,
sk5 @ l2_altcat_1,
inference(cnfConj,[status(thm)],[184]) ).
thf(864,plain,
! [A: $i] :
( ( A != sk5 )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,185]) ).
thf(865,plain,
( ( k1_xboole_0 @ l2_altcat_1 )
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[864:[bind(A,$thf( sk5 ))]]) ).
thf(3364,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[865,233]) ).
thf(3365,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3364]) ).
thf(3366,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3365:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(7453,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,3366]) ).
thf(7454,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7453]) ).
thf(7455,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ( sk5 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7454:[bind(A,$thf( sk5 ))]]) ).
thf(15566,plain,
( ~ $true
| ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( k1_xboole_0 @ l1_altcat_1 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(eqfactor_ordered,[status(thm)],[7455]) ).
thf(15568,plain,
( ( ( sk5 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15566]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(102,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ v3_yellow21 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v1_yellow21 )
& ( A @ k5_waybel34 @ v4_yellow18 )
& ( A @ k5_waybel34 @ v3_yellow18 )
& ( A @ k5_waybel34 @ v2_yellow18 )
& ( A @ k5_waybel34 @ v1_altcat_2 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v9_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel34) ).
thf(595,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ v3_yellow21 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v1_yellow21 )
& ( A @ k5_waybel34 @ v4_yellow18 )
& ( A @ k5_waybel34 @ v3_yellow18 )
& ( A @ k5_waybel34 @ v2_yellow18 )
& ( A @ k5_waybel34 @ v1_altcat_2 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v9_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(596,plain,
! [A: $i] :
( ( ( A @ k5_waybel34 @ v3_yellow21 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v2_yellow21 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v1_yellow21 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v4_yellow18 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v3_yellow18 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v2_yellow18 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v1_altcat_2 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v12_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v11_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v9_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v6_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ v2_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ~ ( A @ k5_waybel34 @ v3_struct_0 )
| ( A @ v2_setfam_1 ) ) ),
inference(cnf,[status(esa)],[595]) ).
thf(597,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v3_yellow18 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(2136,plain,
( ( ( sk29 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true
| ~ ( sk2 @ v1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[628,135]) ).
thf(2137,plain,
( ( ( sk29 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[2136]) ).
thf(2140,plain,
( ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[2137]) ).
thf(10443,plain,
( ( ( sk29 @ v1_orders_2 )
!= ( sk2 @ v1_orders_2 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[638,2140]) ).
thf(10444,plain,
( ( ( sk29 @ v1_orders_2 )
!= ( sk2 @ v1_orders_2 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10443]) ).
thf(10494,plain,
( ( sk29 != sk2 )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10444]) ).
thf(10505,plain,
( ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10494]) ).
thf(10525,plain,
! [A: $i] :
( ( A
!= ( sk2 @ u1_struct_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10505]) ).
thf(10526,plain,
( ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( sk2 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10525:[bind(A,$thf( sk2 @ u1_struct_0 ))]]) ).
thf(13646,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10526]) ).
thf(13647,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13646]) ).
thf(13660,plain,
( ( ( sk2 @ u1_struct_0 )
!= k1_xboole_0 )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13647]) ).
thf(380,plain,
( ( sk17 @ v5_membered )
& ( sk17 @ v4_membered )
& ( sk17 @ v3_membered )
& ( sk17 @ v2_membered )
& ( sk17 @ v1_membered )
& ~ ( sk17 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[379]) ).
thf(385,plain,
sk17 @ v4_membered,
inference(cnfConj,[status(thm)],[380]) ).
thf(384,plain,
sk17 @ v2_membered,
inference(cnfConj,[status(thm)],[380]) ).
thf(3352,plain,
! [A: $i] :
( ( ( sk13 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[260,233]) ).
thf(3353,plain,
! [A: $i] :
( ( ( sk13 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[3352]) ).
thf(3354,plain,
sk13 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[3353:[bind(A,$thf( sk13 ))]]) ).
thf(3378,plain,
! [A: $i] :
( ( ( sk13 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3354,147]) ).
thf(3379,plain,
! [A: $i] :
( ( ( sk13 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3378]) ).
thf(3380,plain,
sk13 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[3379:[bind(A,$thf( sk13 ))]]) ).
thf(3428,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,3380]) ).
thf(3429,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3428:[bind(A,$thf( sk13 ))]]) ).
thf(142,plain,
sk2 @ v1_lattice3,
inference(cnfConj,[status(thm)],[132]) ).
thf(14720,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6744]) ).
thf(14721,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14720]) ).
thf(14726,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ v2_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14721]) ).
thf(143,plain,
sk2 @ v4_orders_2,
inference(cnfConj,[status(thm)],[132]) ).
thf(911,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,143]) ).
thf(912,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[911:[bind(A,$thf( sk2 ))]]) ).
thf(6632,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,912]) ).
thf(6633,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6632]) ).
thf(6634,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6633:[bind(A,$thf( sk2 ))]]) ).
thf(1987,plain,
! [A: $i] :
( ( A != sk23 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,460]) ).
thf(1988,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1987:[bind(A,$thf( sk23 ))]]) ).
thf(5628,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2290]) ).
thf(5629,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 ) ),
inference(simp,[status(thm)],[5628]) ).
thf(5636,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_yellow_0 ) ),
inference(simp,[status(thm)],[5629]) ).
thf(259,plain,
sk13 @ v9_altcat_1,
inference(cnfConj,[status(thm)],[248]) ).
thf(985,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v9_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,259]) ).
thf(986,plain,
( ( k1_xboole_0 @ v9_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[985:[bind(A,$thf( sk13 ))]]) ).
thf(6638,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v9_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,986]) ).
thf(6639,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v9_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6638]) ).
thf(6640,plain,
( ( k1_xboole_0 @ v9_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6639:[bind(A,$thf( sk13 ))]]) ).
thf(668,plain,
sk31 @ v2_lattice3,
inference(cnfConj,[status(thm)],[657]) ).
thf(2563,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,668]) ).
thf(2564,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2563:[bind(A,$thf( sk31 ))]]) ).
thf(6653,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2564]) ).
thf(6654,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6653]) ).
thf(6655,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6654:[bind(A,$thf( sk31 ))]]) ).
thf(4634,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1808]) ).
thf(4635,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[4634]) ).
thf(4638,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[4635]) ).
thf(16,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(196,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(197,plain,
( ~ ( sk6 @ v3_struct_0 )
& ( sk6 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[196]) ).
thf(198,plain,
sk6 @ l1_struct_0,
inference(cnfConj,[status(thm)],[197]) ).
thf(898,plain,
! [A: $i] :
( ( A != sk6 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,198]) ).
thf(899,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk6 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[898:[bind(A,$thf( sk6 ))]]) ).
thf(6697,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk6 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,899]) ).
thf(6698,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk6 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6697]) ).
thf(6699,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk6 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6698:[bind(A,$thf( sk6 ))]]) ).
thf(14082,plain,
! [A: $i] :
( ( ( sk6 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6699,147]) ).
thf(14083,plain,
! [A: $i] :
( ( ( sk6 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[14082]) ).
thf(14084,plain,
( ( sk6 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[14083:[bind(A,$thf( sk6 @ k5_waybel34 ))]]) ).
thf(137,plain,
~ ( sk1 @ v2_setfam_1 ),
inference(cnfConj,[status(thm)],[132]) ).
thf(876,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,137]) ).
thf(877,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[876:[bind(A,$thf( sk1 ))]]) ).
thf(6523,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,877]) ).
thf(6524,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6523]) ).
thf(6525,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( sk1 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6524:[bind(A,$thf( sk1 ))]]) ).
thf(6961,plain,
! [A: $i] :
( ( ( sk1 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(paramod_ordered,[status(thm)],[6525,147]) ).
thf(6962,plain,
! [A: $i] :
( ( ( sk1 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[6961]) ).
thf(6963,plain,
( ( sk1 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(pattern_uni,[status(thm)],[6962:[bind(A,$thf( sk1 @ k5_waybel34 ))]]) ).
thf(7702,plain,
! [A: $i] :
( ( A
!= ( sk1 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6963]) ).
thf(7703,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( sk1 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7702:[bind(A,$thf( sk1 @ k5_waybel34 ))]]) ).
thf(18526,plain,
( ( ( sk1 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,7703]) ).
thf(18527,plain,
( ( ( sk1 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[18526]) ).
thf(18536,plain,
( ( ( sk1 @ k5_waybel34 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[18527]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ u1_altcat_1 @ ( A @ u1_struct_0 @ k2_altcat_1 ) @ ( A @ u1_altcat_1 @ ( A @ u1_altcat_1 @ ( A @ u1_struct_0 @ k3_altcat_1 ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_zfmisc_1 ) ) @ ( A @ u2_altcat_1 @ m3_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_altcat_1) ).
thf(538,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ u1_altcat_1 @ ( A @ u1_struct_0 @ k2_altcat_1 ) @ ( A @ u1_altcat_1 @ ( A @ u1_altcat_1 @ ( A @ u1_struct_0 @ k3_altcat_1 ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_zfmisc_1 ) ) @ ( A @ u2_altcat_1 @ m3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(6,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(153,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)],[6]) ).
thf(6532,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,988]) ).
thf(6533,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6532]) ).
thf(6534,plain,
( ( k1_xboole_0 @ l2_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6533:[bind(A,$thf( sk13 ))]]) ).
thf(10228,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6534,147]) ).
thf(10229,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[10228]) ).
thf(10230,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[10229:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(999,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,869]) ).
thf(1000,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[999]) ).
thf(1001,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[1000]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(377,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(378,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[377]) ).
thf(17490,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,378]) ).
thf(17491,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A @ v1_finset_1 ) ),
inference(simp,[status(thm)],[17490]) ).
thf(17492,plain,
k1_xboole_0 @ v1_finset_1,
inference(pattern_uni,[status(thm)],[17491:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(386,plain,
~ ( sk17 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[380]) ).
thf(6682,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk17 @ v1_xboole_0 ) )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,386]) ).
thf(6683,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk17 @ v1_xboole_0 ) )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6682]) ).
thf(6684,plain,
sk17 @ k5_waybel34 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[6683:[bind(A,$thf( sk17 ))]]) ).
thf(6908,plain,
! [A: $i] :
( ( A
!= ( sk17 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6684]) ).
thf(6909,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk17 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6908:[bind(A,$thf( sk17 @ k5_waybel34 ))]]) ).
thf(4799,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1865]) ).
thf(4800,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[4799]) ).
thf(4803,plain,
( ( sk23 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[4800]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v4_ordinal2 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(436,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v4_ordinal2 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(257,plain,
~ ( sk13 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[248]) ).
thf(141,plain,
( ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3 ),
inference(cnfConj,[status(thm)],[132]) ).
thf(828,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,141]) ).
thf(829,plain,
( ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[828:[bind(A,$thf( sk1 ))]]) ).
thf(3349,plain,
! [A: $i] :
( ( ( sk5 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[185,233]) ).
thf(3350,plain,
! [A: $i] :
( ( ( sk5 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[3349]) ).
thf(3351,plain,
sk5 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[3350:[bind(A,$thf( sk5 ))]]) ).
thf(3368,plain,
! [A: $i] :
( ( ( sk5 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3351,147]) ).
thf(3369,plain,
! [A: $i] :
( ( ( sk5 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3368]) ).
thf(3370,plain,
sk5 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[3369:[bind(A,$thf( sk5 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v2_yellow18 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v2_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_yellow21) ).
thf(168,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v2_yellow18 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v2_yellow18 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( B @ v2_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( A @ ( B @ v3_altcat_2 ) )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[168]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[169]) ).
thf(1091,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,920]) ).
thf(1092,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[1091]) ).
thf(1095,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[1092]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( B @ v3_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(199,plain,
~ ( sk6 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[197]) ).
thf(21967,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk6 @ v3_struct_0 ) )
| ~ $true
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[423,199]) ).
thf(21968,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk6 @ v3_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[21967]) ).
thf(21969,plain,
( ~ ( sk6 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk6 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[21968:[bind(A,$thf( sk6 ))]]) ).
thf(25453,plain,
( ~ ( sk6 @ u1_struct_0 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[21969,198]) ).
thf(25454,plain,
~ ( sk6 @ u1_struct_0 @ v1_xboole_0 ),
inference(simp,[status(thm)],[25453]) ).
thf(25455,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk6 @ u1_struct_0 @ v1_xboole_0 ) )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,25454]) ).
thf(25456,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk6 @ u1_struct_0 @ v1_xboole_0 ) )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[25455]) ).
thf(25457,plain,
sk6 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[25456:[bind(A,$thf( sk6 @ u1_struct_0 ))]]) ).
thf(36,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(301,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)],[36]) ).
thf(420,plain,
sk21 @ v3_lattice3,
inference(cnfConj,[status(thm)],[412]) ).
thf(414,plain,
sk21 @ v1_orders_2,
inference(cnfConj,[status(thm)],[412]) ).
thf(1116,plain,
( ( ( sk21 @ v1_orders_2 )
!= ( sk2 @ v1_orders_2 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v3_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[414,135]) ).
thf(1117,plain,
( ( ( sk21 @ v1_orders_2 )
!= ( sk2 @ v1_orders_2 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[1116]) ).
thf(1120,plain,
( ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[1117]) ).
thf(9677,plain,
( ( ( sk21 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[420,1120]) ).
thf(9678,plain,
( ( ( sk21 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9677]) ).
thf(9708,plain,
( ( sk21 != sk2 )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9678]) ).
thf(9712,plain,
( ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9708]) ).
thf(9738,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,9712]) ).
thf(9739,plain,
( ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[9738:[bind(A,$thf( sk2 ))]]) ).
thf(11758,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,9739]) ).
thf(11759,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11758]) ).
thf(11772,plain,
( ( sk2 != k1_xboole_0 )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11759]) ).
thf(15293,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk2 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,11772]) ).
thf(15294,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15293]) ).
thf(15295,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15294:[bind(A,$thf( sk21 ))]]) ).
thf(7330,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6634]) ).
thf(7331,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7330:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(16973,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,7331]) ).
thf(16974,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[16973]) ).
thf(16979,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ v4_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[16974]) ).
thf(186,plain,
~ ( sk5 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[184]) ).
thf(917,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,186]) ).
thf(918,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[917:[bind(A,$thf( sk5 ))]]) ).
thf(6712,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,918]) ).
thf(6713,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6712]) ).
thf(6714,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk5 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6713:[bind(A,$thf( sk5 ))]]) ).
thf(14610,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6714,147]) ).
thf(14611,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[14610]) ).
thf(14612,plain,
( ( sk5 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[14611:[bind(A,$thf( sk5 @ k5_waybel34 ))]]) ).
thf(660,plain,
sk31 @ v2_yellow_0,
inference(cnfConj,[status(thm)],[657]) ).
thf(2399,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v2_yellow_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,660]) ).
thf(2400,plain,
( ( k1_xboole_0 @ v2_yellow_0 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2399:[bind(A,$thf( sk31 ))]]) ).
thf(10529,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10505]) ).
thf(10530,plain,
( ( sk29 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10529:[bind(A,$thf( sk1 ))]]) ).
thf(6481,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2309]) ).
thf(6482,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6481]) ).
thf(6483,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6482:[bind(A,$thf( sk29 ))]]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(387,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_funct_1 )
| ~ ( A @ ( B @ m1_pboole ) ) )
& ( ( B @ v1_relat_1 )
| ~ ( A @ ( B @ m1_pboole ) ) ) ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( B @ v1_relat_1 )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[388]) ).
thf(1111,plain,
! [A: $i] :
( ( ( sk19 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[404,147]) ).
thf(1112,plain,
! [A: $i] :
( ( ( sk19 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[1111]) ).
thf(1113,plain,
sk19 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[1112:[bind(A,$thf( sk19 ))]]) ).
thf(2634,plain,
! [A: $i] :
( ( A != sk19 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,1113]) ).
thf(2635,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk19 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2634:[bind(A,$thf( sk19 ))]]) ).
thf(6514,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk19 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2635]) ).
thf(6515,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk19 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6514]) ).
thf(6516,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk19 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6515:[bind(A,$thf( sk19 ))]]) ).
thf(9445,plain,
! [A: $i] :
( ( ( sk19 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6516,147]) ).
thf(9446,plain,
! [A: $i] :
( ( ( sk19 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[9445]) ).
thf(9447,plain,
( ( sk19 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[9446:[bind(A,$thf( sk19 @ k5_waybel34 ))]]) ).
thf(3385,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,3354]) ).
thf(3386,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3385:[bind(A,$thf( sk13 ))]]) ).
thf(7608,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,3386]) ).
thf(7609,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7608]) ).
thf(7610,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7609:[bind(A,$thf( sk13 ))]]) ).
thf(15672,plain,
( ~ $true
| ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( k1_xboole_0 @ l1_altcat_1 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(eqfactor_ordered,[status(thm)],[7610]) ).
thf(15674,plain,
( ( ( sk13 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15672]) ).
thf(6517,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk9 @ v1_xboole_0 ) )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,211]) ).
thf(6518,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk9 @ v1_xboole_0 ) )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6517]) ).
thf(6519,plain,
sk9 @ k5_waybel34 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[6518:[bind(A,$thf( sk9 ))]]) ).
thf(6891,plain,
! [A: $i] :
( ( A
!= ( sk9 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6519]) ).
thf(6892,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk9 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6891:[bind(A,$thf( sk9 @ k5_waybel34 ))]]) ).
thf(2146,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,629]) ).
thf(2147,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2146:[bind(A,$thf( sk29 ))]]) ).
thf(6550,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2147]) ).
thf(6551,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6550]) ).
thf(6552,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6551:[bind(A,$thf( sk29 ))]]) ).
thf(637,plain,
sk29 @ v3_orders_2,
inference(cnfConj,[status(thm)],[624]) ).
thf(2296,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,637]) ).
thf(2297,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2296:[bind(A,$thf( sk29 ))]]) ).
thf(6724,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2297]) ).
thf(6725,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6724]) ).
thf(6726,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6725:[bind(A,$thf( sk29 ))]]) ).
thf(14688,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6726,147]) ).
thf(14689,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[14688]) ).
thf(14690,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(pattern_uni,[status(thm)],[14689:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(128,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(785,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)],[128]) ).
thf(816,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,142]) ).
thf(817,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[816:[bind(A,$thf( sk2 ))]]) ).
thf(6505,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,817]) ).
thf(6506,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6505]) ).
thf(6507,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6506:[bind(A,$thf( sk2 ))]]) ).
thf(6749,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6507,147]) ).
thf(6750,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[6749]) ).
thf(6751,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(pattern_uni,[status(thm)],[6750:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(7682,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6751]) ).
thf(7683,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7682:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(6721,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,940]) ).
thf(6722,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6721]) ).
thf(6723,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6722:[bind(A,$thf( sk29 ))]]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(587,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v1_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v1_yellow21 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_yellow21) ).
thf(338,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v1_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v1_yellow21 )
& ( A @ ( B @ v3_altcat_2 ) )
& ( B @ v1_altcat_2 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( A @ ( B @ v3_altcat_2 ) )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[338]) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[339]) ).
thf(252,plain,
sk13 @ v3_yellow21,
inference(cnfConj,[status(thm)],[248]) ).
thf(933,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v3_yellow21 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,252]) ).
thf(934,plain,
( ( k1_xboole_0 @ v3_yellow21 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( sk13 ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ? [B: $i] : ( A @ ( B @ m1_altcat_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_altcat_2) ).
thf(399,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ? [B: $i] : ( A @ ( B @ m1_altcat_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(400,plain,
! [A: $i] :
( ( A @ ( A @ sk18 @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[399]) ).
thf(19893,plain,
! [A: $i] :
( ( ( sk13 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ ( A @ sk18 @ m1_altcat_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[260,400]) ).
thf(19894,plain,
! [A: $i] :
( ( ( sk13 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ ( A @ sk18 @ m1_altcat_2 ) ) ),
inference(simp,[status(thm)],[19893]) ).
thf(19895,plain,
sk13 @ ( sk13 @ sk18 @ m1_altcat_2 ),
inference(pattern_uni,[status(thm)],[19894:[bind(A,$thf( sk13 ))]]) ).
thf(664,plain,
sk31 @ l1_orders_2,
inference(cnfConj,[status(thm)],[657]) ).
thf(2500,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,664]) ).
thf(2501,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2500:[bind(A,$thf( sk31 ))]]) ).
thf(947,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,817]) ).
thf(948,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[947]) ).
thf(949,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[948]) ).
thf(254,plain,
sk13 @ v6_altcat_1,
inference(cnfConj,[status(thm)],[248]) ).
thf(937,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v6_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,254]) ).
thf(938,plain,
( ( k1_xboole_0 @ v6_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( sk13 ))]]) ).
thf(3705,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v6_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,938]) ).
thf(3706,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v6_altcat_1 ) ),
inference(simp,[status(thm)],[3705]) ).
thf(3713,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v6_altcat_1 ) ),
inference(simp,[status(thm)],[3706]) ).
thf(6880,plain,
! [A: $i] :
( ( ( sk9 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6519,147]) ).
thf(6881,plain,
! [A: $i] :
( ( ( sk9 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[6880]) ).
thf(6882,plain,
sk9 @ k5_waybel34 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[6881:[bind(A,$thf( sk9 @ k5_waybel34 ))]]) ).
thf(6922,plain,
! [A: $i] :
( ( A
!= ( sk9 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6882]) ).
thf(6923,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk9 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6922:[bind(A,$thf( sk9 @ k5_waybel34 ))]]) ).
thf(15176,plain,
( ( ( sk9 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6923]) ).
thf(15177,plain,
( ( ( sk9 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15176]) ).
thf(15182,plain,
( ( ( sk9 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15177]) ).
thf(634,plain,
sk29 @ v1_yellow_0,
inference(cnfConj,[status(thm)],[624]) ).
thf(2275,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v1_yellow_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,634]) ).
thf(2276,plain,
( ( k1_xboole_0 @ v1_yellow_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2275:[bind(A,$thf( sk29 ))]]) ).
thf(6679,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2276]) ).
thf(6680,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6679]) ).
thf(6681,plain,
( ( k1_xboole_0 @ v1_yellow_0 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6680:[bind(A,$thf( sk29 ))]]) ).
thf(661,plain,
~ ( sk31 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[657]) ).
thf(941,plain,
! [A: $i] :
( ( A != sk31 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,661]) ).
thf(942,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[941:[bind(A,$thf( sk31 ))]]) ).
thf(6544,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,942]) ).
thf(6545,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6544]) ).
thf(6546,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6545:[bind(A,$thf( sk31 ))]]) ).
thf(12289,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6546,147]) ).
thf(12290,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[12289]) ).
thf(12291,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[12290:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(606,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v2_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( B @ v2_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(416,plain,
~ ( sk21 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[412]) ).
thf(9740,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,9712]) ).
thf(9741,plain,
( ( sk21 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[9740:[bind(A,$thf( sk1 ))]]) ).
thf(11813,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,9741]) ).
thf(11814,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11813]) ).
thf(11827,plain,
( ( sk1 != k1_xboole_0 )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11814]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v3_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow21 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow21) ).
thf(289,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v3_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow21 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(448,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(21726,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk21 @ v3_struct_0 ) )
| ~ $true
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[423,416]) ).
thf(21727,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk21 @ v3_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[21726]) ).
thf(21728,plain,
( ~ ( sk21 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk21 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[21727:[bind(A,$thf( sk21 ))]]) ).
thf(413,plain,
sk21 @ l1_orders_2,
inference(cnfConj,[status(thm)],[412]) ).
thf(25573,plain,
! [A: $i] :
( ( ( sk21 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[413,430]) ).
thf(25574,plain,
! [A: $i] :
( ( ( sk21 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25573]) ).
thf(25575,plain,
sk21 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25574:[bind(A,$thf( sk21 ))]]) ).
thf(25648,plain,
( ~ ( sk21 @ u1_struct_0 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[21728,25575]) ).
thf(25649,plain,
~ ( sk21 @ u1_struct_0 @ v1_xboole_0 ),
inference(simp,[status(thm)],[25648]) ).
thf(26154,plain,
( ( ( sk21 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,25649]) ).
thf(26155,plain,
( ( sk21 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26154]) ).
thf(26160,plain,
( ( sk21 @ u1_struct_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[26155]) ).
thf(1874,plain,
! [A: $i] :
( ( A != sk23 )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,457]) ).
thf(1875,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1874:[bind(A,$thf( sk23 ))]]) ).
thf(6732,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6489,147]) ).
thf(6733,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[6732]) ).
thf(6734,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(pattern_uni,[status(thm)],[6733:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(261,plain,
sk13 @ v3_yellow18,
inference(cnfConj,[status(thm)],[248]) ).
thf(418,plain,
sk21 @ v2_lattice3,
inference(cnfConj,[status(thm)],[412]) ).
thf(1735,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,418]) ).
thf(1736,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1735:[bind(A,$thf( sk21 ))]]) ).
thf(6547,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1736]) ).
thf(6548,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6547]) ).
thf(6549,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6548:[bind(A,$thf( sk21 ))]]) ).
thf(11262,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6549,147]) ).
thf(11263,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[11262]) ).
thf(11264,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(pattern_uni,[status(thm)],[11263:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(5195,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2147]) ).
thf(5196,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[5195]) ).
thf(5199,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[5196]) ).
thf(1114,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,413]) ).
thf(1115,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1114:[bind(A,$thf( sk21 ))]]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow21) ).
thf(314,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(315,plain,
! [A: $i] :
( ( ( A @ v1_yellow21 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v4_yellow18 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v3_yellow18 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v2_yellow18 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v1_altcat_2 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v12_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v11_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v9_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ~ ( A @ v3_struct_0 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ) ),
inference(cnf,[status(esa)],[314]) ).
thf(325,plain,
! [A: $i] :
( ( A @ v2_yellow18 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(21921,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk29 @ v3_struct_0 ) )
| ~ $true
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[423,631]) ).
thf(21922,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk29 @ v3_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[21921]) ).
thf(21923,plain,
( ~ ( sk29 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk29 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[21922:[bind(A,$thf( sk29 ))]]) ).
thf(625,plain,
sk29 @ l1_orders_2,
inference(cnfConj,[status(thm)],[624]) ).
thf(25564,plain,
! [A: $i] :
( ( ( sk29 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[625,430]) ).
thf(25565,plain,
! [A: $i] :
( ( ( sk29 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25564]) ).
thf(25566,plain,
sk29 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25565:[bind(A,$thf( sk29 ))]]) ).
thf(25630,plain,
( ~ ( sk29 @ u1_struct_0 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[21923,25566]) ).
thf(25631,plain,
~ ( sk29 @ u1_struct_0 @ v1_xboole_0 ),
inference(simp,[status(thm)],[25630]) ).
thf(25711,plain,
( ( ( sk29 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,25631]) ).
thf(25712,plain,
( ( sk29 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[25711]) ).
thf(25717,plain,
( ( sk29 @ u1_struct_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[25712]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 )
| ~ ( C @ v1_finset_1 )
| ~ ( B @ v1_finset_1 )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[151]) ).
thf(255,plain,
sk13 @ v2_yellow21,
inference(cnfConj,[status(thm)],[248]) ).
thf(943,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v2_yellow21 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,255]) ).
thf(944,plain,
( ( k1_xboole_0 @ v2_yellow21 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( sk13 ))]]) ).
thf(3726,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,944]) ).
thf(3727,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow21 ) ),
inference(simp,[status(thm)],[3726]) ).
thf(3734,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_yellow21 ) ),
inference(simp,[status(thm)],[3727]) ).
thf(228,plain,
! [A: $i] :
( ~ ( A @ k5_waybel34 @ v3_struct_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(166,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(167,plain,
! [A: $i] :
( ( A @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[166]) ).
thf(1845,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A @ v1_funct_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,167]) ).
thf(1846,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[1845]) ).
thf(1847,plain,
k1_xboole_0 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[1846:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(179,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,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(443,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)],[67]) ).
thf(321,plain,
! [A: $i] :
( ( A @ v3_yellow18 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(4811,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1875]) ).
thf(4812,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[4811]) ).
thf(4815,plain,
( ( sk23 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[4812]) ).
thf(73,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(480,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)],[73]) ).
thf(662,plain,
sk31 @ v3_orders_2,
inference(cnfConj,[status(thm)],[657]) ).
thf(2406,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,662]) ).
thf(2407,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2406:[bind(A,$thf( sk31 ))]]) ).
thf(6668,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2407]) ).
thf(6669,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6668]) ).
thf(6670,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6669:[bind(A,$thf( sk31 ))]]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(591,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(646,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(253,plain,
sk13 @ v4_yellow18,
inference(cnfConj,[status(thm)],[248]) ).
thf(348,plain,
! [A: $i] :
( ( A @ v2_membered )
| ~ ( A @ v3_membered ) ),
inference(cnf,[status(esa)],[347]) ).
thf(10200,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10025]) ).
thf(10201,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10200:[bind(A,$thf( sk23 ))]]) ).
thf(145,plain,
sk2 @ l1_orders_2,
inference(cnfConj,[status(thm)],[132]) ).
thf(907,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,145]) ).
thf(908,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( sk2 ))]]) ).
thf(6715,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,908]) ).
thf(6716,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6715]) ).
thf(6717,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6716:[bind(A,$thf( sk2 ))]]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_altcat_1 ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_altcat_1) ).
thf(397,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_altcat_1 ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(251,plain,
sk13 @ v11_altcat_1,
inference(cnfConj,[status(thm)],[248]) ).
thf(931,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v11_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,251]) ).
thf(932,plain,
( ( k1_xboole_0 @ v11_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[931:[bind(A,$thf( sk13 ))]]) ).
thf(6629,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v11_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,932]) ).
thf(6630,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v11_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6629]) ).
thf(6631,plain,
( ( k1_xboole_0 @ v11_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6630:[bind(A,$thf( sk13 ))]]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( B @ v3_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(633,plain,
sk29 @ v25_waybel_0,
inference(cnfConj,[status(thm)],[624]) ).
thf(2202,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v25_waybel_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,633]) ).
thf(2203,plain,
( ( k1_xboole_0 @ v25_waybel_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2202:[bind(A,$thf( sk29 ))]]) ).
thf(5362,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v25_waybel_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2203]) ).
thf(5363,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v25_waybel_0 ) ),
inference(simp,[status(thm)],[5362]) ).
thf(5370,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v25_waybel_0 ) ),
inference(simp,[status(thm)],[5363]) ).
thf(9742,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,9712]) ).
thf(9743,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[9742:[bind(A,$thf( sk21 ))]]) ).
thf(1118,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,414]) ).
thf(1119,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1118:[bind(A,$thf( sk21 ))]]) ).
thf(6496,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2400]) ).
thf(6497,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6496]) ).
thf(6498,plain,
( ( k1_xboole_0 @ v2_yellow_0 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6497:[bind(A,$thf( sk31 ))]]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v11_altcat_1 )
& ( B @ v9_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_yellow21) ).
thf(391,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ v11_altcat_1 )
& ( B @ v9_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( ( B @ v11_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v9_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v9_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v9_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ( B @ v2_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v9_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v9_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[391]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( B @ v11_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v9_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[392]) ).
thf(2001,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,625]) ).
thf(2002,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( sk29 ))]]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_waybel34) ).
thf(424,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_orders_2 )
& ( B @ v2_lattice3 )
& ( B @ v1_lattice3 )
& ( B @ v4_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ m2_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ l1_orders_2 )
| ~ ( B @ v2_lattice3 )
| ~ ( B @ v1_lattice3 )
| ~ ( B @ v4_orders_2 )
| ~ ( B @ v3_orders_2 )
| ~ ( B @ v2_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ v4_orders_2 )
| ~ ( A @ v3_orders_2 )
| ~ ( A @ v2_orders_2 ) )
& ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ l1_orders_2 )
| ~ ( B @ v2_lattice3 )
| ~ ( B @ v1_lattice3 )
| ~ ( B @ v4_orders_2 )
| ~ ( B @ v3_orders_2 )
| ~ ( B @ v2_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ v4_orders_2 )
| ~ ( A @ v3_orders_2 )
| ~ ( A @ v2_orders_2 ) )
& ( ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ l1_orders_2 )
| ~ ( B @ v2_lattice3 )
| ~ ( B @ v1_lattice3 )
| ~ ( B @ v4_orders_2 )
| ~ ( B @ v3_orders_2 )
| ~ ( B @ v2_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ v4_orders_2 )
| ~ ( A @ v3_orders_2 )
| ~ ( A @ v2_orders_2 ) ) ),
inference(cnf,[status(esa)],[424]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ m2_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ l1_orders_2 )
| ~ ( B @ v2_lattice3 )
| ~ ( B @ v1_lattice3 )
| ~ ( B @ v4_orders_2 )
| ~ ( B @ v3_orders_2 )
| ~ ( B @ v2_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ v4_orders_2 )
| ~ ( A @ v3_orders_2 )
| ~ ( A @ v2_orders_2 ) ),
inference(cnfConj,[status(thm)],[425]) ).
thf(8,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(162,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(163,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A != B ) )
& ( A @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[162]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ( A = B )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 )
| ( A = B ) ),
inference(lifteq,[status(thm)],[164]) ).
thf(9731,plain,
! [B: $i,A: $i] :
( ( B != sk21 )
| ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[165,9712]) ).
thf(9732,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[9731:[bind(A,$thf( A )),bind(B,$thf( sk21 ))]]) ).
thf(9744,plain,
( ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9732]) ).
thf(12121,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[194,9744]) ).
thf(12122,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12121]) ).
thf(12133,plain,
( ( sk21 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12122]) ).
thf(935,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v4_yellow18 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,253]) ).
thf(936,plain,
( ( k1_xboole_0 @ v4_yellow18 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( sk13 ))]]) ).
thf(6614,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_yellow18 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,936]) ).
thf(6615,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_yellow18 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6614]) ).
thf(6616,plain,
( ( k1_xboole_0 @ v4_yellow18 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6615:[bind(A,$thf( sk13 ))]]) ).
thf(630,plain,
sk29 @ v24_waybel_0,
inference(cnfConj,[status(thm)],[624]) ).
thf(2153,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v24_waybel_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,630]) ).
thf(2154,plain,
( ( k1_xboole_0 @ v24_waybel_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2153:[bind(A,$thf( sk29 ))]]) ).
thf(19,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(204,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(205,plain,
( ( sk8 @ v2_funct_1 )
& ( sk8 @ v1_funct_1 )
& ( sk8 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[204]) ).
thf(206,plain,
sk8 @ v1_relat_1,
inference(cnfConj,[status(thm)],[205]) ).
thf(6472,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk25 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1995]) ).
thf(6473,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk25 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6472]) ).
thf(6474,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( sk25 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6473:[bind(A,$thf( sk25 ))]]) ).
thf(602,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v11_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(665,plain,
sk31 @ v1_yellow_0,
inference(cnfConj,[status(thm)],[657]) ).
thf(2507,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v1_yellow_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,665]) ).
thf(2508,plain,
( ( k1_xboole_0 @ v1_yellow_0 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2507:[bind(A,$thf( sk31 ))]]) ).
thf(658,plain,
sk31 @ v3_lattice3,
inference(cnfConj,[status(thm)],[657]) ).
thf(2384,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,658]) ).
thf(2385,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2384:[bind(A,$thf( sk31 ))]]) ).
thf(6700,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2385]) ).
thf(6701,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6700]) ).
thf(6702,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6701:[bind(A,$thf( sk31 ))]]) ).
thf(25585,plain,
! [A: $i] :
( ( ( sk2 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[145,430]) ).
thf(25586,plain,
! [A: $i] :
( ( ( sk2 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25585]) ).
thf(25587,plain,
sk2 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25586:[bind(A,$thf( sk2 ))]]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_altcat_1) ).
thf(236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(237,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C = F )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
& ( ( B = E )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
& ( ( A = D )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ) ),
inference(cnf,[status(esa)],[236]) ).
thf(240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[237]) ).
thf(243,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
| ( C = F )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(7504,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6717]) ).
thf(7505,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7504:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(6508,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1875]) ).
thf(6509,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6508]) ).
thf(6510,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6509:[bind(A,$thf( sk23 ))]]) ).
thf(9046,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6510,147]) ).
thf(9047,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[9046]) ).
thf(9048,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[9047:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(7319,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6634,147]) ).
thf(7320,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[7319]) ).
thf(7321,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(pattern_uni,[status(thm)],[7320:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(862,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v1_yellow21 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,249]) ).
thf(863,plain,
( ( k1_xboole_0 @ v1_yellow21 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( sk13 ))]]) ).
thf(2914,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,863]) ).
thf(2915,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow21 ) ),
inference(simp,[status(thm)],[2914]) ).
thf(2922,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_yellow21 ) ),
inference(simp,[status(thm)],[2915]) ).
thf(290,plain,
! [A: $i] :
( ( ( A @ v2_yellow21 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v1_altcat_2 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v12_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v11_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ( A @ v2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ~ ( A @ v3_struct_0 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ) ),
inference(cnf,[status(esa)],[289]) ).
thf(292,plain,
! [A: $i] :
( ( A @ v2_yellow21 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[290]) ).
thf(47,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(351,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(352,plain,
( ( sk16 @ v1_funct_1 )
& ( sk16 @ v1_xboole_0 )
& ( sk16 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[351]) ).
thf(354,plain,
sk16 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[352]) ).
thf(1905,plain,
( ( ( sk16 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,918]) ).
thf(1906,plain,
( ( ( sk16 @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1905]) ).
thf(1907,plain,
( ( sk16 != sk5 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1906]) ).
thf(1032,plain,
! [A: $i] :
( ( ( sk16 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[354,150]) ).
thf(1033,plain,
! [A: $i] :
( ( ( sk16 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[1032]) ).
thf(1034,plain,
sk16 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[1033:[bind(A,$thf( sk16 ))]]) ).
thf(3301,plain,
( ( sk5 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(rewrite,[status(thm)],[1907,1034]) ).
thf(114,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(678,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)],[114]) ).
thf(4476,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1729]) ).
thf(4477,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[4476]) ).
thf(4480,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[4477]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ m1_pboole ) )
| ~ ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(381,plain,
sk17 @ v5_membered,
inference(cnfConj,[status(thm)],[380]) ).
thf(208,plain,
sk8 @ v2_funct_1,
inference(cnfConj,[status(thm)],[205]) ).
thf(888,plain,
! [A: $i] :
( ( A != sk8 )
| ( k1_xboole_0 @ v2_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,208]) ).
thf(889,plain,
( ( k1_xboole_0 @ v2_funct_1 )
| ~ ( sk8 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( sk8 ))]]) ).
thf(6569,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk8 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_funct_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,889]) ).
thf(6570,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk8 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_funct_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6569]) ).
thf(6571,plain,
( ( k1_xboole_0 @ v2_funct_1 )
| ( sk8 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6570:[bind(A,$thf( sk8 ))]]) ).
thf(663,plain,
sk31 @ v2_orders_2,
inference(cnfConj,[status(thm)],[657]) ).
thf(2448,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,663]) ).
thf(2449,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2448:[bind(A,$thf( sk31 ))]]) ).
thf(6656,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2449]) ).
thf(6657,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6656]) ).
thf(6658,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6657:[bind(A,$thf( sk31 ))]]) ).
thf(13517,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6658,147]) ).
thf(13518,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[13517]) ).
thf(13519,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(pattern_uni,[status(thm)],[13518:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(3402,plain,
! [A: $i] :
( ( A != sk5 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,3370]) ).
thf(3403,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3402:[bind(A,$thf( sk5 ))]]) ).
thf(7623,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,3403]) ).
thf(7624,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7623]) ).
thf(7625,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk5 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7624:[bind(A,$thf( sk5 ))]]) ).
thf(15871,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7625,147]) ).
thf(15872,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15871]) ).
thf(15873,plain,
( ( sk5 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[15872:[bind(A,$thf( sk5 @ k5_waybel34 ))]]) ).
thf(4319,plain,
( ( ( sk19 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1110]) ).
thf(4320,plain,
( ( ( sk19 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[4319]) ).
thf(4323,plain,
( ( sk19 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[4320]) ).
thf(13834,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10530]) ).
thf(13835,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13834]) ).
thf(13848,plain,
( ( sk1 != k1_xboole_0 )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13835]) ).
thf(87,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(529,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)],[87]) ).
thf(6007,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2508]) ).
thf(6008,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 ) ),
inference(simp,[status(thm)],[6007]) ).
thf(6015,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_yellow_0 ) ),
inference(simp,[status(thm)],[6008]) ).
thf(22,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(215,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)],[22]) ).
thf(216,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)],[215]) ).
thf(218,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)],[216]) ).
thf(220,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)],[218]) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(12060,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,9743]) ).
thf(12061,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12060]) ).
thf(12073,plain,
( ( sk21 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12061]) ).
thf(15540,plain,
! [A: $i] :
( ( A
!= ( sk11 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,7440]) ).
thf(15541,plain,
! [A: $i] :
( ( A
!= ( sk11 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15540]) ).
thf(15542,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk11 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15541:[bind(A,$thf( sk11 @ k5_waybel34 ))]]) ).
thf(6650,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow21 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,944]) ).
thf(6651,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow21 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6650]) ).
thf(6652,plain,
( ( k1_xboole_0 @ v2_yellow21 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6651:[bind(A,$thf( sk13 ))]]) ).
thf(43,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(334,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(21705,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk13 @ v3_struct_0 ) )
| ~ $true
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[423,257]) ).
thf(21706,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk13 @ v3_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[21705]) ).
thf(21707,plain,
( ~ ( sk13 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk13 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[21706:[bind(A,$thf( sk13 ))]]) ).
thf(22135,plain,
( ~ ( sk13 @ u1_struct_0 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[21707,3380]) ).
thf(22136,plain,
~ ( sk13 @ u1_struct_0 @ v1_xboole_0 ),
inference(simp,[status(thm)],[22135]) ).
thf(6572,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1012]) ).
thf(6573,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6572]) ).
thf(6574,plain,
( ( k1_xboole_0 @ v2_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6573:[bind(A,$thf( sk13 ))]]) ).
thf(12383,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6574,147]) ).
thf(12384,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_altcat_1 ) ),
inference(simp,[status(thm)],[12383]) ).
thf(12385,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[12384:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(4985,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2002]) ).
thf(4986,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4985]) ).
thf(4989,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4986]) ).
thf(458,plain,
sk23 @ v3_orders_2,
inference(cnfConj,[status(thm)],[454]) ).
thf(1882,plain,
! [A: $i] :
( ( A != sk23 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,458]) ).
thf(1883,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( sk23 ))]]) ).
thf(6563,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1883]) ).
thf(6564,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6563]) ).
thf(6565,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6564:[bind(A,$thf( sk23 ))]]) ).
thf(10181,plain,
! [B: $i,A: $i] :
( ( A != sk23 )
| ( B != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[165,10025]) ).
thf(10182,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10181:[bind(A,$thf( sk23 ))]]) ).
thf(10205,plain,
( ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10182]) ).
thf(13360,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10205]) ).
thf(13361,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13360]) ).
thf(13374,plain,
( ( sk23 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13361]) ).
thf(17588,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk23 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,13374]) ).
thf(17589,plain,
( ( sk23 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[17588:[bind(A,$thf( sk2 ))]]) ).
thf(17599,plain,
( ( sk23 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[17589]) ).
thf(824,plain,
! [A: $i] :
( ( A
!= ( sk2 @ u1_struct_0 ) )
| ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| sk3
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,141]) ).
thf(825,plain,
( ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| sk3
| ~ ( sk2 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[824:[bind(A,$thf( sk2 @ u1_struct_0 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( B @ l2_altcat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_altcat_2) ).
thf(349,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_altcat_2 ) )
=> ( B @ l2_altcat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(455,plain,
sk23 @ v4_orders_2,
inference(cnfConj,[status(thm)],[454]) ).
thf(1855,plain,
! [A: $i] :
( ( A != sk23 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,455]) ).
thf(1856,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1855:[bind(A,$thf( sk23 ))]]) ).
thf(6578,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1856]) ).
thf(6579,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6578]) ).
thf(6580,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6579:[bind(A,$thf( sk23 ))]]) ).
thf(12548,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6580,147]) ).
thf(12549,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[12548]) ).
thf(12550,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(pattern_uni,[status(thm)],[12549:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(6526,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1119]) ).
thf(6527,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6526]) ).
thf(6528,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6527:[bind(A,$thf( sk21 ))]]) ).
thf(93,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(561,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)],[93]) ).
thf(7313,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6583]) ).
thf(7314,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7313:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(16459,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,7314]) ).
thf(16460,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[16459]) ).
thf(16465,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ v2_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[16460]) ).
thf(34,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(297,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15529,plain,
! [A: $i] :
( ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[7440,147]) ).
thf(15530,plain,
! [A: $i] :
( ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15529]) ).
thf(15531,plain,
( ( sk11 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[15530:[bind(A,$thf( sk11 @ k5_waybel34 ))]]) ).
thf(192,plain,
k1_xboole_0 @ v3_membered,
inference(cnfConj,[status(thm)],[189]) ).
thf(59,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(407,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)],[59]) ).
thf(7638,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,3429]) ).
thf(7639,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7638]) ).
thf(7640,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7639:[bind(A,$thf( sk13 ))]]) ).
thf(15561,plain,
! [A: $i] :
( ( A
!= ( sk5 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,7455]) ).
thf(15562,plain,
! [A: $i] :
( ( A
!= ( sk5 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15561]) ).
thf(15563,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk5 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15562:[bind(A,$thf( sk5 @ k5_waybel34 ))]]) ).
thf(250,plain,
sk13 @ v2_yellow18,
inference(cnfConj,[status(thm)],[248]) ).
thf(913,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v2_yellow18 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,250]) ).
thf(914,plain,
( ( k1_xboole_0 @ v2_yellow18 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( sk13 ))]]) ).
thf(6694,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow18 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,914]) ).
thf(6695,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow18 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6694]) ).
thf(6696,plain,
( ( k1_xboole_0 @ v2_yellow18 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6695:[bind(A,$thf( sk13 ))]]) ).
thf(5979,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2449]) ).
thf(5980,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[5979]) ).
thf(5983,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[5980]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(356,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(357,plain,
! [A: $i] :
( ( ( A @ v5_membered )
| ~ ( A @ v1_xboole_0 ) )
& ( ( A @ v4_membered )
| ~ ( A @ v1_xboole_0 ) )
& ( ( A @ v3_membered )
| ~ ( A @ v1_xboole_0 ) )
& ( ( A @ v2_membered )
| ~ ( A @ v1_xboole_0 ) )
& ( ( A @ v1_membered )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[356]) ).
thf(361,plain,
! [A: $i] :
( ( A @ v3_membered )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(854,plain,
! [A: $i] :
( ( A != sk6 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,199]) ).
thf(855,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk6 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( sk6 ))]]) ).
thf(6662,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk6 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,855]) ).
thf(6663,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk6 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6662]) ).
thf(6664,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk6 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6663:[bind(A,$thf( sk6 ))]]) ).
thf(13560,plain,
! [A: $i] :
( ( ( sk6 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6664,147]) ).
thf(13561,plain,
! [A: $i] :
( ( ( sk6 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[13560]) ).
thf(13562,plain,
( ( sk6 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[13561:[bind(A,$thf( sk6 @ k5_waybel34 ))]]) ).
thf(818,plain,
! [A: $i] :
( ( A != sk21 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,416]) ).
thf(819,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[818:[bind(A,$thf( sk21 ))]]) ).
thf(1025,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,819]) ).
thf(1026,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1027,plain,
( ( sk21 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1026]) ).
thf(58,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(405,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(406,plain,
! [A: $i] : ( A @ ( A @ sk20 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[405]) ).
thf(144,plain,
( ~ ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| sk3 ),
inference(cnfConj,[status(thm)],[132]) ).
thf(2735,plain,
! [A: $i] :
( ( ( A @ ( A @ sk20 @ m1_subset_1 ) )
!= ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) ) )
| ~ $true
| sk3 ),
inference(paramod_ordered,[status(thm)],[406,144]) ).
thf(2736,plain,
! [A: $i] :
( ( ( A @ ( A @ sk20 @ m1_subset_1 ) )
!= ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) ) )
| sk3 ),
inference(simp,[status(thm)],[2735]) ).
thf(2739,plain,
! [A: $i] :
( ( A
!= ( sk1 @ k9_waybel34 @ u1_struct_0 ) )
| ( ( A @ sk20 )
!= sk2 )
| sk3 ),
inference(simp,[status(thm)],[2736]) ).
thf(2741,plain,
( ( ( sk1 @ k9_waybel34 @ u1_struct_0 @ sk20 )
!= sk2 )
| sk3 ),
inference(simp,[status(thm)],[2739]) ).
thf(324,plain,
! [A: $i] :
( ( A @ v1_yellow21 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(235,plain,
sk12 @ l1_struct_0,
inference(cnf,[status(esa)],[234]) ).
thf(921,plain,
! [A: $i] :
( ( A != sk12 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,235]) ).
thf(922,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk12 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( sk12 ))]]) ).
thf(6644,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk12 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,922]) ).
thf(6645,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk12 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6644]) ).
thf(6646,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk12 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6645:[bind(A,$thf( sk12 ))]]) ).
thf(229,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v12_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(5383,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2276]) ).
thf(5384,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 ) ),
inference(simp,[status(thm)],[5383]) ).
thf(5391,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_yellow_0 ) ),
inference(simp,[status(thm)],[5384]) ).
thf(75,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(484,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)],[75]) ).
thf(826,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| sk3
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,141]) ).
thf(827,plain,
( ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| sk3
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( sk2 ))]]) ).
thf(10622,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,827]) ).
thf(10623,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[10622]) ).
thf(10634,plain,
( ( sk2 != k1_xboole_0 )
| ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[10623]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_yellow21 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_yellow21) ).
thf(433,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_yellow21 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(434,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k3_yellow21 ) )
= B )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[433]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ k3_yellow21 ) )
= B ) ),
inference(lifteq,[status(thm)],[434]) ).
thf(187,plain,
sk5 @ v1_altcat_2,
inference(cnfConj,[status(thm)],[184]) ).
thf(886,plain,
! [A: $i] :
( ( A != sk5 )
| ( k1_xboole_0 @ v1_altcat_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,187]) ).
thf(887,plain,
( ( k1_xboole_0 @ v1_altcat_2 )
| ~ ( sk5 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( sk5 ))]]) ).
thf(3129,plain,
( ( ( sk5 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,887]) ).
thf(3130,plain,
( ( ( sk5 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(simp,[status(thm)],[3129]) ).
thf(3137,plain,
( ( sk5 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(simp,[status(thm)],[3130]) ).
thf(25493,plain,
! [A: $i] :
( ( ( sk6 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25457,147]) ).
thf(25494,plain,
! [A: $i] :
( ( ( sk6 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25493]) ).
thf(25495,plain,
sk6 @ u1_struct_0 @ k5_waybel34 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25494:[bind(A,$thf( sk6 @ u1_struct_0 @ k5_waybel34 ))]]) ).
thf(822,plain,
! [A: $i] :
( ( A != sk23 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,461]) ).
thf(823,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[822:[bind(A,$thf( sk23 ))]]) ).
thf(6659,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,823]) ).
thf(6660,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6659]) ).
thf(6661,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6660:[bind(A,$thf( sk23 ))]]) ).
thf(13534,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6661,147]) ).
thf(13535,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[13534]) ).
thf(13536,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[13535:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( A @ ( C @ m1_pboole ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
<=> ( D @ ( C @ r1_altcat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_altcat_2) ).
thf(326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( A @ ( C @ m1_pboole ) ) )
=> ( ( ( D @ ( C @ r1_altcat_2 ) )
=> ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
=> ( D @ ( C @ r1_altcat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
| ~ ( D @ ( C @ r1_altcat_2 ) )
| ~ ( B @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) ) )
& ( ( D @ ( C @ r1_altcat_2 ) )
| ~ ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
| ~ ( B @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) ) ) ),
inference(cnf,[status(esa)],[326]) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
| ~ ( D @ ( C @ r1_altcat_2 ) )
| ~ ( B @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(6706,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,865]) ).
thf(6707,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6706]) ).
thf(6708,plain,
( ( k1_xboole_0 @ l2_altcat_1 )
| ( sk5 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6707:[bind(A,$thf( sk5 ))]]) ).
thf(13068,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6619,147]) ).
thf(13069,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[13068]) ).
thf(13070,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(pattern_uni,[status(thm)],[13069:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(583,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_yellow21 ) )
= ( B @ k1_yellow21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_yellow21) ).
thf(522,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_yellow21 ) )
= ( B @ k1_yellow21 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(21756,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk31 @ v3_struct_0 ) )
| ~ $true
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[423,661]) ).
thf(21757,plain,
! [A: $i] :
( ( ( A @ v3_struct_0 )
!= ( sk31 @ v3_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[21756]) ).
thf(21758,plain,
( ~ ( sk31 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk31 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[21757:[bind(A,$thf( sk31 ))]]) ).
thf(25600,plain,
! [A: $i] :
( ( ( sk31 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[664,430]) ).
thf(25601,plain,
! [A: $i] :
( ( ( sk31 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25600]) ).
thf(25602,plain,
sk31 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25601:[bind(A,$thf( sk31 ))]]) ).
thf(26129,plain,
( ~ ( sk31 @ u1_struct_0 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[21758,25602]) ).
thf(26130,plain,
~ ( sk31 @ u1_struct_0 @ v1_xboole_0 ),
inference(simp,[status(thm)],[26129]) ).
thf(6490,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1988]) ).
thf(6491,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6490]) ).
thf(6492,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6491:[bind(A,$thf( sk23 ))]]) ).
thf(8179,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6492,147]) ).
thf(8180,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[8179]) ).
thf(8181,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[8180:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(134,plain,
( ( sk2 @ v1_orders_2 )
| sk3 ),
inference(cnfConj,[status(thm)],[132]) ).
thf(830,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,134]) ).
thf(831,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| sk3
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[830:[bind(A,$thf( sk2 ))]]) ).
thf(6626,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,831]) ).
thf(6627,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6626]) ).
thf(6628,plain,
( ( k1_xboole_0 @ v1_orders_2 )
| sk3
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6627:[bind(A,$thf( sk2 ))]]) ).
thf(10065,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_orders_2 )
| sk3 ),
inference(paramod_ordered,[status(thm)],[6628,147]) ).
thf(10066,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3 ),
inference(simp,[status(thm)],[10065]) ).
thf(10067,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3 ),
inference(pattern_uni,[status(thm)],[10066:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(123,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(757,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)],[123]) ).
thf(3918,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v9_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,986]) ).
thf(3919,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v9_altcat_1 ) ),
inference(simp,[status(thm)],[3918]) ).
thf(3926,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v9_altcat_1 ) ),
inference(simp,[status(thm)],[3919]) ).
thf(6599,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,819]) ).
thf(6600,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6599]) ).
thf(6601,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6600:[bind(A,$thf( sk21 ))]]) ).
thf(12861,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6601,147]) ).
thf(12862,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[12861]) ).
thf(12863,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[12862:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(2514,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v3_yellow_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,666]) ).
thf(2515,plain,
( ( k1_xboole_0 @ v3_yellow_0 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2514:[bind(A,$thf( sk31 ))]]) ).
thf(6987,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6543,147]) ).
thf(6988,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[6987]) ).
thf(6989,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(pattern_uni,[status(thm)],[6988:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(7961,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6989]) ).
thf(7962,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7961:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(6475,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1729]) ).
thf(6476,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6475]) ).
thf(6477,plain,
( ( k1_xboole_0 @ v3_orders_2 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6476:[bind(A,$thf( sk21 ))]]) ).
thf(659,plain,
sk31 @ v4_orders_2,
inference(cnfConj,[status(thm)],[657]) ).
thf(2392,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,659]) ).
thf(2393,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2392:[bind(A,$thf( sk31 ))]]) ).
thf(5807,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2393]) ).
thf(5808,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[5807]) ).
thf(5811,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[5808]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( B @ ( A @ k1_altcat_1 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_altcat_4) ).
thf(593,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( B @ ( A @ k1_altcat_1 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(103,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(610,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)],[103]) ).
thf(154,plain,
( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(miniscope,[status(thm)],[153]) ).
thf(155,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( F @ m2_relset_1 ) ) )
| ~ ( E @ ( D @ ( F @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(615,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(15667,plain,
! [A: $i] :
( ( A
!= ( sk13 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,7610]) ).
thf(15668,plain,
! [A: $i] :
( ( A
!= ( sk13 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15667]) ).
thf(15669,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk13 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15668:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(256,plain,
sk13 @ v1_altcat_2,
inference(cnfConj,[status(thm)],[248]) ).
thf(981,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v1_altcat_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,256]) ).
thf(982,plain,
( ( k1_xboole_0 @ v1_altcat_2 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[981:[bind(A,$thf( sk13 ))]]) ).
thf(6718,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,982]) ).
thf(6719,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6718]) ).
thf(6720,plain,
( ( k1_xboole_0 @ v1_altcat_2 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6719:[bind(A,$thf( sk13 ))]]) ).
thf(5329,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v24_waybel_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2154]) ).
thf(5330,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v24_waybel_0 ) ),
inference(simp,[status(thm)],[5329]) ).
thf(5337,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v24_waybel_0 ) ),
inference(simp,[status(thm)],[5330]) ).
thf(14108,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6702,147]) ).
thf(14109,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[14108]) ).
thf(14110,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(pattern_uni,[status(thm)],[14109:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(10194,plain,
! [A: $i] :
( ( A
!= ( sk2 @ u1_struct_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10025]) ).
thf(10195,plain,
( ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( sk2 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10194:[bind(A,$thf( sk2 @ u1_struct_0 ))]]) ).
thf(6499,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2501]) ).
thf(6500,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6499]) ).
thf(6501,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6500:[bind(A,$thf( sk31 ))]]) ).
thf(212,plain,
sk9 @ v1_finset_1,
inference(cnfConj,[status(thm)],[210]) ).
thf(328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ r1_altcat_2 ) )
| ~ ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
| ~ ( B @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(76,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(488,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)],[76]) ).
thf(415,plain,
sk21 @ v2_orders_2,
inference(cnfConj,[status(thm)],[412]) ).
thf(1145,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,415]) ).
thf(1146,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( sk21 ))]]) ).
thf(6596,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1146]) ).
thf(6597,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6596]) ).
thf(6598,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6597:[bind(A,$thf( sk21 ))]]) ).
thf(12766,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6598,147]) ).
thf(12767,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[12766]) ).
thf(12768,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(pattern_uni,[status(thm)],[12767:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(225,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v2_yellow21 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(1751,plain,
! [A: $i] :
( ( A != sk21 )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,420]) ).
thf(1752,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ~ ( sk21 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1751:[bind(A,$thf( sk21 ))]]) ).
thf(6608,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1752]) ).
thf(6609,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6608]) ).
thf(6610,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6609:[bind(A,$thf( sk21 ))]]) ).
thf(12904,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6610,147]) ).
thf(12905,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[12904]) ).
thf(12906,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(pattern_uni,[status(thm)],[12905:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(193,plain,
k1_xboole_0 @ v5_membered,
inference(cnfConj,[status(thm)],[189]) ).
thf(10527,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10505]) ).
thf(10528,plain,
( ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10527:[bind(A,$thf( sk2 ))]]) ).
thf(112,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(669,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)],[112]) ).
thf(258,plain,
sk13 @ v12_altcat_1,
inference(cnfConj,[status(thm)],[248]) ).
thf(983,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v12_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,258]) ).
thf(984,plain,
( ( k1_xboole_0 @ v12_altcat_1 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[983:[bind(A,$thf( sk13 ))]]) ).
thf(6584,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v12_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,984]) ).
thf(6585,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v12_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6584]) ).
thf(6586,plain,
( ( k1_xboole_0 @ v12_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6585:[bind(A,$thf( sk13 ))]]) ).
thf(12637,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v12_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6586,147]) ).
thf(12638,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v12_altcat_1 ) ),
inference(simp,[status(thm)],[12637]) ).
thf(12639,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v12_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[12638:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(71,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(476,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)],[71]) ).
thf(10531,plain,
! [A: $i] :
( ( A != sk29 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10505]) ).
thf(10532,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10531:[bind(A,$thf( sk29 ))]]) ).
thf(14176,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10532]) ).
thf(14177,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[14176]) ).
thf(14189,plain,
( ( sk29 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[14177]) ).
thf(6944,plain,
! [A: $i] :
( ( ( sk25 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6474,147]) ).
thf(6945,plain,
! [A: $i] :
( ( ( sk25 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[6944]) ).
thf(6946,plain,
( ( sk25 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[6945:[bind(A,$thf( sk25 @ k5_waybel34 ))]]) ).
thf(4440,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1115]) ).
thf(4441,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4440]) ).
thf(4444,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4441]) ).
thf(6623,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow21 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,863]) ).
thf(6624,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow21 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6623]) ).
thf(6625,plain,
( ( k1_xboole_0 @ v1_yellow21 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6624:[bind(A,$thf( sk13 ))]]) ).
thf(7975,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,7304]) ).
thf(7976,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7975:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(7647,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,3429]) ).
thf(7648,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[7647]) ).
thf(7651,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[7648]) ).
thf(298,plain,
! [A: $i] : ( A @ ( A @ sk14 @ m1_pboole ) ),
inference(cnf,[status(esa)],[297]) ).
thf(17711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,389]) ).
thf(17712,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_relat_1 ) ),
inference(simp,[status(thm)],[17711]) ).
thf(17713,plain,
! [A: $i] : ( A @ sk14 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[17712:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk14 ))]]) ).
thf(17720,plain,
! [A: $i] : ( A @ sk14 @ v1_relat_1 ),
inference(simp,[status(thm)],[17713]) ).
thf(1121,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,823]) ).
thf(1122,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1121]) ).
thf(1131,plain,
( ( sk23 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1122]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(569,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(3684,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_yellow18 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,936]) ).
thf(3685,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_yellow18 ) ),
inference(simp,[status(thm)],[3684]) ).
thf(3692,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_yellow18 ) ),
inference(simp,[status(thm)],[3685]) ).
thf(6182,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2564]) ).
thf(6183,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[6182]) ).
thf(6186,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[6183]) ).
thf(7493,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6717,147]) ).
thf(7494,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[7493]) ).
thf(7495,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[7494:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(8218,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,7495]) ).
thf(8219,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8218:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(25676,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ u1_struct_0 @ v1_xboole_0 ) )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,25610]) ).
thf(25677,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ u1_struct_0 @ v1_xboole_0 ) )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[25676]) ).
thf(25678,plain,
sk23 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[25677:[bind(A,$thf( sk23 @ u1_struct_0 ))]]) ).
thf(7483,plain,
! [A: $i] :
( ( A
!= ( sk19 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6480]) ).
thf(7484,plain,
! [A: $i] :
( ( A
!= ( sk19 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7483]) ).
thf(7485,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk19 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7484:[bind(A,$thf( sk19 @ k5_waybel34 ))]]) ).
thf(3361,plain,
! [A: $i] :
( ( ( sk11 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,233]) ).
thf(3362,plain,
! [A: $i] :
( ( ( sk11 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[3361]) ).
thf(3363,plain,
sk11 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[3362:[bind(A,$thf( sk11 ))]]) ).
thf(3388,plain,
! [A: $i] :
( ( ( sk11 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3363,147]) ).
thf(3389,plain,
! [A: $i] :
( ( ( sk11 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3388]) ).
thf(3390,plain,
sk11 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[3389:[bind(A,$thf( sk11 ))]]) ).
thf(10576,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,825]) ).
thf(10577,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[10576]) ).
thf(10588,plain,
( ( ( sk2 @ u1_struct_0 )
!= k1_xboole_0 )
| ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[10577]) ).
thf(459,plain,
sk23 @ v2_orders_2,
inference(cnfConj,[status(thm)],[454]) ).
thf(1915,plain,
! [A: $i] :
( ( A != sk23 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,459]) ).
thf(1916,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ~ ( sk23 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1915:[bind(A,$thf( sk23 ))]]) ).
thf(4949,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1916]) ).
thf(4950,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[4949]) ).
thf(4953,plain,
( ( sk23 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[4950]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( B @ v2_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(12817,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10195]) ).
thf(12818,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12817]) ).
thf(12831,plain,
( ( ( sk2 @ u1_struct_0 )
!= k1_xboole_0 )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12818]) ).
thf(81,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k9_waybel34 @ m1_altcat_2 ) )
& ( A @ k5_waybel34 @ ( A @ k9_waybel34 @ v3_altcat_2 ) )
& ( A @ k9_waybel34 @ v6_altcat_1 )
& ( A @ k9_waybel34 @ v2_altcat_1 )
& ~ ( A @ k9_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_waybel34) ).
thf(503,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k9_waybel34 @ m1_altcat_2 ) )
& ( A @ k5_waybel34 @ ( A @ k9_waybel34 @ v3_altcat_2 ) )
& ( A @ k9_waybel34 @ v6_altcat_1 )
& ( A @ k9_waybel34 @ v2_altcat_1 )
& ~ ( A @ k9_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(605,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v4_yellow18 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(3747,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,982]) ).
thf(3748,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(simp,[status(thm)],[3747]) ).
thf(3755,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(simp,[status(thm)],[3748]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_altcat_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_altcat_2) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_altcat_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(3555,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,934]) ).
thf(3556,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow21 ) ),
inference(simp,[status(thm)],[3555]) ).
thf(3563,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_yellow21 ) ),
inference(simp,[status(thm)],[3556]) ).
thf(504,plain,
! [A: $i] :
( ( ( A @ k5_waybel34 @ ( A @ k9_waybel34 @ m1_altcat_2 ) )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k5_waybel34 @ ( A @ k9_waybel34 @ v3_altcat_2 ) )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k9_waybel34 @ v6_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ( A @ k9_waybel34 @ v2_altcat_1 )
| ( A @ v2_setfam_1 ) )
& ( ~ ( A @ k9_waybel34 @ v3_struct_0 )
| ( A @ v2_setfam_1 ) ) ),
inference(cnf,[status(esa)],[503]) ).
thf(508,plain,
! [A: $i] :
( ( A @ k9_waybel34 @ v2_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[504]) ).
thf(6590,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v6_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,938]) ).
thf(6591,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v6_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6590]) ).
thf(6592,plain,
( ( k1_xboole_0 @ v6_altcat_1 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6591:[bind(A,$thf( sk13 ))]]) ).
thf(632,plain,
sk29 @ v4_orders_2,
inference(cnfConj,[status(thm)],[624]) ).
thf(2160,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,632]) ).
thf(2161,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2160:[bind(A,$thf( sk29 ))]]) ).
thf(6611,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2161]) ).
thf(6612,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6611]) ).
thf(6613,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6612:[bind(A,$thf( sk29 ))]]) ).
thf(12921,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6613,147]) ).
thf(12922,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[12921]) ).
thf(12923,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(pattern_uni,[status(thm)],[12922:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_altcat_1 ) ) @ m1_pboole ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[397]) ).
thf(15550,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[7455,147]) ).
thf(15551,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15550]) ).
thf(15552,plain,
( ( sk5 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[15551:[bind(A,$thf( sk5 @ k5_waybel34 ))]]) ).
thf(22137,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ u1_struct_0 @ v1_xboole_0 ) )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,22136]) ).
thf(22138,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ u1_struct_0 @ v1_xboole_0 ) )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[22137]) ).
thf(22139,plain,
sk13 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[22138:[bind(A,$thf( sk13 @ u1_struct_0 ))]]) ).
thf(22175,plain,
! [A: $i] :
( ( ( sk13 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22139,147]) ).
thf(22176,plain,
! [A: $i] :
( ( ( sk13 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[22175]) ).
thf(22177,plain,
sk13 @ u1_struct_0 @ k5_waybel34 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[22176:[bind(A,$thf( sk13 @ u1_struct_0 @ k5_waybel34 ))]]) ).
thf(127,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(773,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)],[127]) ).
thf(136,plain,
( ( sk2 @ v3_lattice3 )
| sk3 ),
inference(cnfConj,[status(thm)],[132]) ).
thf(925,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,136]) ).
thf(926,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| sk3
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[925:[bind(A,$thf( sk2 ))]]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( B @ v1_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[339]) ).
thf(6976,plain,
! [A: $i] :
( ( A
!= ( sk1 @ k5_waybel34 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6525]) ).
thf(6977,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6976:[bind(A,$thf( sk1 @ k5_waybel34 ))]]) ).
thf(15339,plain,
( ( ( sk1 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6977]) ).
thf(15340,plain,
( ( ( sk1 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15339]) ).
thf(15349,plain,
( ( ( sk1 @ k5_waybel34 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15340]) ).
thf(13439,plain,
! [A: $i] :
( ( ( sk12 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6646,147]) ).
thf(13440,plain,
! [A: $i] :
( ( ( sk12 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[13439]) ).
thf(13441,plain,
( ( sk12 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[13440:[bind(A,$thf( sk12 @ k5_waybel34 ))]]) ).
thf(19330,plain,
! [A: $i] :
( ( A
!= ( sk12 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,13441]) ).
thf(19331,plain,
! [A: $i] :
( ( A
!= ( sk12 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[19330]) ).
thf(19332,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk12 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19331:[bind(A,$thf( sk12 @ k5_waybel34 ))]]) ).
thf(360,plain,
! [A: $i] :
( ( A @ v4_membered )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(8204,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,7321]) ).
thf(8205,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8204:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(6484,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1808]) ).
thf(6485,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6484]) ).
thf(6486,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6485:[bind(A,$thf( sk21 ))]]) ).
thf(6605,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2393]) ).
thf(6606,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6605]) ).
thf(6607,plain,
( ( k1_xboole_0 @ v4_orders_2 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6606:[bind(A,$thf( sk31 ))]]) ).
thf(12887,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6607,147]) ).
thf(12888,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[12887]) ).
thf(12889,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(pattern_uni,[status(thm)],[12888:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(1797,plain,
( ( ( sk26 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,885]) ).
thf(1798,plain,
( ( ( sk26 @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[1797]) ).
thf(1799,plain,
( ( sk26 != sk16 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[1798]) ).
thf(3173,plain,
( ( sk26 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(rewrite,[status(thm)],[1799,1034]) ).
thf(11522,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6552,147]) ).
thf(11523,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[11522]) ).
thf(11524,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(pattern_uni,[status(thm)],[11523:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(122,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [B: $i] :
( ( ( A @ k5_waybel34 @ ( B @ m1_altcat_2 ) )
& ( A @ k5_waybel34 @ ( B @ v3_altcat_2 ) )
& ( B @ v6_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B
= ( A @ k9_waybel34 ) )
<=> ( ! [C: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F = D )
& ( E = C ) )
=> ( ! [G: $i] :
( ( D @ ( C @ ( A @ k5_waybel34 @ k1_altcat_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ k1_altcat_1 ) ) @ ( G @ r2_hidden ) )
<=> ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( G @ ( D @ ( C @ ( A @ k5_waybel34 @ k5_yellow21 ) ) ) @ ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ k2_waybel34 ) ) @ v22_waybel_0 ) ) ) ) )
| ( ( D @ ( C @ ( A @ k5_waybel34 @ k1_altcat_1 ) ) )
= k1_xboole_0 ) ) ) ) ) ) )
& ! [C: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel34) ).
thf(718,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [B: $i] :
( ( ( A @ k5_waybel34 @ ( B @ m1_altcat_2 ) )
& ( A @ k5_waybel34 @ ( B @ v3_altcat_2 ) )
& ( B @ v6_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F = D )
& ( E = C ) )
=> ( ! [G: $i] :
( ( D @ ( C @ ( A @ k5_waybel34 @ k1_altcat_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( G @ ( D @ ( C @ ( A @ k5_waybel34 @ k5_yellow21 ) ) ) @ ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ k2_waybel34 ) ) @ v22_waybel_0 ) ) )
=> ( F @ ( E @ ( B @ k1_altcat_1 ) ) @ ( G @ r2_hidden ) ) )
& ( ( F @ ( E @ ( B @ k1_altcat_1 ) ) @ ( G @ r2_hidden ) )
=> ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( G @ ( D @ ( C @ ( A @ k5_waybel34 @ k5_yellow21 ) ) ) @ ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ k2_waybel34 ) ) @ v22_waybel_0 ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ k5_waybel34 @ k1_altcat_1 ) ) )
= k1_xboole_0 ) ) ) ) ) ) )
& ! [C: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) )
=> ( B
= ( A @ k9_waybel34 ) ) )
& ( ( B
= ( A @ k9_waybel34 ) )
=> ( ! [C: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F = D )
& ( E = C ) )
=> ( ! [G: $i] :
( ( D @ ( C @ ( A @ k5_waybel34 @ k1_altcat_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( G @ ( D @ ( C @ ( A @ k5_waybel34 @ k5_yellow21 ) ) ) @ ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ k2_waybel34 ) ) @ v22_waybel_0 ) ) )
=> ( F @ ( E @ ( B @ k1_altcat_1 ) ) @ ( G @ r2_hidden ) ) )
& ( ( F @ ( E @ ( B @ k1_altcat_1 ) ) @ ( G @ r2_hidden ) )
=> ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( G @ ( D @ ( C @ ( A @ k5_waybel34 @ k5_yellow21 ) ) ) @ ( C @ ( A @ k5_waybel34 @ k3_yellow21 ) @ ( D @ ( A @ k5_waybel34 @ k3_yellow21 ) @ k2_waybel34 ) ) @ v22_waybel_0 ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ k5_waybel34 @ k1_altcat_1 ) ) )
= k1_xboole_0 ) ) ) ) ) ) )
& ! [C: $i] :
( ( A @ k5_waybel34 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(627,plain,
sk29 @ v2_orders_2,
inference(cnfConj,[status(thm)],[624]) ).
thf(2063,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,627]) ).
thf(2064,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2063:[bind(A,$thf( sk29 ))]]) ).
thf(6635,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2064]) ).
thf(6636,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6635]) ).
thf(6637,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6636:[bind(A,$thf( sk29 ))]]) ).
thf(14636,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(paramod_ordered,[status(thm)],[6720,147]) ).
thf(14637,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(simp,[status(thm)],[14636]) ).
thf(14638,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(pattern_uni,[status(thm)],[14637:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(25667,plain,
! [A: $i] :
( ( ( sk2 @ l1_struct_0 )
!= ( A @ l1_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ~ $true
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[25587,423]) ).
thf(25668,plain,
! [A: $i] :
( ( ( sk2 @ l1_struct_0 )
!= ( A @ l1_struct_0 ) )
| ~ ( A @ u1_struct_0 @ v1_xboole_0 )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[25667]) ).
thf(25669,plain,
( ~ ( sk2 @ u1_struct_0 @ v1_xboole_0 )
| ( sk2 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[25668:[bind(A,$thf( sk2 ))]]) ).
thf(30,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(263,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)],[30]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
| ~ ( B @ v1_finset_1 )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[263]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( A @ ( C @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_altcat_2) ).
thf(159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( A @ ( C @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(160,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( B @ ( D @ m1_pboole ) )
& ( A @ ( C @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) ),
inference(miniscope,[status(thm)],[159]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
| ~ ( B @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(7632,plain,
( ( ( sk5 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,3403]) ).
thf(7633,plain,
( ( ( sk5 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[7632]) ).
thf(7636,plain,
( ( sk5 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[7633]) ).
thf(26208,plain,
( ( ( sk31 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,26130]) ).
thf(26209,plain,
( ( sk31 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26208]) ).
thf(26214,plain,
( ( sk31 @ u1_struct_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[26209]) ).
thf(6566,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,916]) ).
thf(6567,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6566]) ).
thf(6568,plain,
( ( k1_xboole_0 @ l2_altcat_1 )
| ( sk11 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6567:[bind(A,$thf( sk11 ))]]) ).
thf(12166,plain,
! [A: $i] :
( ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6568,147]) ).
thf(12167,plain,
! [A: $i] :
( ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[12166]) ).
thf(12168,plain,
( ( sk11 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[12167:[bind(A,$thf( sk11 @ k5_waybel34 ))]]) ).
thf(10198,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10025]) ).
thf(10199,plain,
( ( sk23 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10198:[bind(A,$thf( sk1 ))]]) ).
thf(13027,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10199]) ).
thf(13028,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13027]) ).
thf(13041,plain,
( ( sk1 != k1_xboole_0 )
| ( sk23 != sk2 )
| ~ sk3
| ~ ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13028]) ).
thf(14043,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_yellow18 ) ),
inference(paramod_ordered,[status(thm)],[6696,147]) ).
thf(14044,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_yellow18 ) ),
inference(simp,[status(thm)],[14043]) ).
thf(14045,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_yellow18 ) ),
inference(pattern_uni,[status(thm)],[14044:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(19961,plain,
! [A: $i] :
( ( ( sk11 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ ( A @ sk18 @ m1_altcat_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,400]) ).
thf(19962,plain,
! [A: $i] :
( ( ( sk11 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ ( A @ sk18 @ m1_altcat_2 ) ) ),
inference(simp,[status(thm)],[19961]) ).
thf(19963,plain,
sk11 @ ( sk11 @ sk18 @ m1_altcat_2 ),
inference(pattern_uni,[status(thm)],[19962:[bind(A,$thf( sk11 ))]]) ).
thf(10512,plain,
! [B: $i,A: $i] :
( ( A != sk29 )
| ( B != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[165,10505]) ).
thf(10513,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10512:[bind(A,$thf( sk29 ))]]) ).
thf(10536,plain,
( ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10513]) ).
thf(14245,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk29 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10536]) ).
thf(14246,plain,
( ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk29 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[14245:[bind(A,$thf( sk2 ))]]) ).
thf(14254,plain,
( ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk29 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[14246]) ).
thf(180,plain,
! [A: $i] :
( ( A @ v1_membered )
| ~ ( A @ v2_membered ) ),
inference(cnf,[status(esa)],[179]) ).
thf(3150,plain,
( ( ( sk8 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_funct_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,889]) ).
thf(3151,plain,
( ( ( sk8 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_funct_1 ) ),
inference(simp,[status(thm)],[3150]) ).
thf(3158,plain,
( ( sk8 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_funct_1 ) ),
inference(simp,[status(thm)],[3151]) ).
thf(601,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v6_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(3503,plain,
! [A: $i] :
( ( A != sk11 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,3390]) ).
thf(3504,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3503:[bind(A,$thf( sk11 ))]]) ).
thf(11834,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6565,147]) ).
thf(11835,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[11834]) ).
thf(11836,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(pattern_uni,[status(thm)],[11835:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(5840,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2407]) ).
thf(5841,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[5840]) ).
thf(5844,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[5841]) ).
thf(12315,plain,
! [A: $i] :
( ( ( sk8 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[6571,147]) ).
thf(12316,plain,
! [A: $i] :
( ( ( sk8 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_funct_1 ) ),
inference(simp,[status(thm)],[12315]) ).
thf(12317,plain,
( ( sk8 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_funct_1 ) ),
inference(pattern_uni,[status(thm)],[12316:[bind(A,$thf( sk8 @ k5_waybel34 ))]]) ).
thf(5823,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2400]) ).
thf(5824,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow_0 ) ),
inference(simp,[status(thm)],[5823]) ).
thf(5831,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_yellow_0 ) ),
inference(simp,[status(thm)],[5824]) ).
thf(5346,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2161]) ).
thf(5347,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[5346]) ).
thf(5350,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[5347]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[169]) ).
thf(7285,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6477,147]) ).
thf(7286,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[7285]) ).
thf(7287,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(pattern_uni,[status(thm)],[7286:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(7936,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6486,147]) ).
thf(7937,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[7936]) ).
thf(7938,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(pattern_uni,[status(thm)],[7937:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(191,plain,
k1_xboole_0 @ v2_membered,
inference(cnfConj,[status(thm)],[189]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(401,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(402,plain,
! [A: $i] :
( ( A @ v4_membered )
| ~ ( A @ v5_membered ) ),
inference(cnf,[status(esa)],[401]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(8695,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6501,147]) ).
thf(8696,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[8695]) ).
thf(8697,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[8696:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(6602,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1916]) ).
thf(6603,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk23 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6602]) ).
thf(6604,plain,
( ( k1_xboole_0 @ v2_orders_2 )
| ( sk23 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6603:[bind(A,$thf( sk23 ))]]) ).
thf(12838,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6604,147]) ).
thf(12839,plain,
! [A: $i] :
( ( ( sk23 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[12838]) ).
thf(12840,plain,
( ( sk23 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(pattern_uni,[status(thm)],[12839:[bind(A,$thf( sk23 @ k5_waybel34 ))]]) ).
thf(97,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(579,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)],[97]) ).
thf(5795,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2385]) ).
thf(5796,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[5795]) ).
thf(5799,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[5796]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( B @ v9_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(667,plain,
sk31 @ v1_lattice3,
inference(cnfConj,[status(thm)],[657]) ).
thf(2521,plain,
! [A: $i] :
( ( A != sk31 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,667]) ).
thf(2522,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ~ ( sk31 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2521:[bind(A,$thf( sk31 ))]]) ).
thf(6703,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2522]) ).
thf(6704,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6703]) ).
thf(6705,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6704:[bind(A,$thf( sk31 ))]]) ).
thf(382,plain,
sk17 @ v1_membered,
inference(cnfConj,[status(thm)],[380]) ).
thf(6665,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,887]) ).
thf(6666,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk5 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_altcat_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6665]) ).
thf(6667,plain,
( ( k1_xboole_0 @ v1_altcat_2 )
| ( sk5 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6666:[bind(A,$thf( sk5 ))]]) ).
thf(13370,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk23 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,10205]) ).
thf(13371,plain,
( ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk23 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13370:[bind(A,$thf( sk2 ))]]) ).
thf(13380,plain,
( ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk23 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13371]) ).
thf(9736,plain,
! [A: $i] :
( ( A
!= ( sk2 @ u1_struct_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,9712]) ).
thf(9737,plain,
( ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( sk2 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[9736:[bind(A,$thf( sk2 @ u1_struct_0 ))]]) ).
thf(11501,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,9737]) ).
thf(11502,plain,
( ( ( sk2 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11501]) ).
thf(11515,plain,
( ( ( sk2 @ u1_struct_0 )
!= k1_xboole_0 )
| ( sk21 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11502]) ).
thf(2045,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,942]) ).
thf(2046,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2045]) ).
thf(2055,plain,
( ( sk31 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2046]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(181,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_yellow21 ) @ l1_orders_2 )
& ( B @ ( A @ k3_yellow21 ) @ v2_lattice3 )
& ( B @ ( A @ k3_yellow21 ) @ v1_lattice3 )
& ( B @ ( A @ k3_yellow21 ) @ v4_orders_2 )
& ( B @ ( A @ k3_yellow21 ) @ v3_orders_2 )
& ( B @ ( A @ k3_yellow21 ) @ v2_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow21) ).
thf(704,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_yellow21 ) @ l1_orders_2 )
& ( B @ ( A @ k3_yellow21 ) @ v2_lattice3 )
& ( B @ ( A @ k3_yellow21 ) @ v1_lattice3 )
& ( B @ ( A @ k3_yellow21 ) @ v4_orders_2 )
& ( B @ ( A @ k3_yellow21 ) @ v3_orders_2 )
& ( B @ ( A @ k3_yellow21 ) @ v2_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ ( A @ k2_altcat_1 ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_altcat_1) ).
thf(330,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ ( A @ k2_altcat_1 ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ ( A @ k2_altcat_1 ) @ m1_pboole ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[330]) ).
thf(10673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ m1_pboole ) )
!= ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) ) )
| ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) @ ( C @ ( B @ k2_altcat_1 ) @ m1_pboole ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,331]) ).
thf(10674,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ m1_pboole ) )
!= ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) ) )
| ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) @ ( C @ ( B @ k2_altcat_1 ) @ m1_pboole ) ) ),
inference(simp,[status(thm)],[10673]) ).
thf(10675,plain,
! [A: $i] : ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[10674:[bind(A,$thf( F @ ( F @ k2_zfmisc_1 ) )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ k2_zfmisc_1 ) @ sk14 ))]]) ).
thf(10741,plain,
! [A: $i] : ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ m1_pboole ) ),
inference(simp,[status(thm)],[10675]) ).
thf(7739,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,3504]) ).
thf(7740,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7739]) ).
thf(7741,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk11 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7740:[bind(A,$thf( sk11 ))]]) ).
thf(16041,plain,
! [A: $i] :
( ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7741,147]) ).
thf(16042,plain,
! [A: $i] :
( ( ( sk11 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16041]) ).
thf(16043,plain,
( ( sk11 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[16042:[bind(A,$thf( sk11 @ k5_waybel34 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_functor0) ).
thf(310,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(311,plain,
! [A: $i] :
( ( ( A @ v1_altcat_2 )
| ~ ( A @ v12_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) )
& ( ~ ( A @ v3_struct_0 )
| ~ ( A @ v12_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ) ),
inference(cnf,[status(esa)],[310]) ).
thf(313,plain,
! [A: $i] :
( ( A @ v1_altcat_2 )
| ~ ( A @ v12_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[311]) ).
thf(6897,plain,
! [A: $i] :
( ( ( sk17 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6684,147]) ).
thf(6898,plain,
! [A: $i] :
( ( ( sk17 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[6897]) ).
thf(6899,plain,
sk17 @ k5_waybel34 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[6898:[bind(A,$thf( sk17 @ k5_waybel34 ))]]) ).
thf(6936,plain,
! [A: $i] :
( ( A
!= ( sk17 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6899]) ).
thf(6937,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk17 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6936:[bind(A,$thf( sk17 @ k5_waybel34 ))]]) ).
thf(15199,plain,
( ( ( sk17 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6937]) ).
thf(15200,plain,
( ( ( sk17 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15199]) ).
thf(15205,plain,
( ( ( sk17 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15200]) ).
thf(350,plain,
! [B: $i,A: $i] :
( ( B @ l2_altcat_1 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[349]) ).
thf(90,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(540,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)],[90]) ).
thf(13383,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6637,147]) ).
thf(13384,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[13383]) ).
thf(13385,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(pattern_uni,[status(thm)],[13384:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k1_altcat_1 ) ) @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( B @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ k3_yellow21 ) @ ( B @ ( A @ k3_yellow21 ) @ ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ v5_orders_3 ) ) )
& ( C @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( B @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_yellow21) ).
thf(672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k1_altcat_1 ) ) @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_altcat_1 )
& ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( B @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ k3_yellow21 ) @ ( B @ ( A @ k3_yellow21 ) @ ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ v5_orders_3 ) ) )
& ( C @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( B @ ( A @ k3_yellow21 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k5_yellow21 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(604,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v12_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(25468,plain,
( ( ( sk6 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,25454]) ).
thf(25469,plain,
( ( sk6 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[25468]) ).
thf(25474,plain,
( ( sk6 @ u1_struct_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[25469]) ).
thf(509,plain,
! [A: $i] :
( ( A @ k9_waybel34 @ v6_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[504]) ).
thf(12129,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,9744]) ).
thf(12130,plain,
( ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12129:[bind(A,$thf( sk2 ))]]) ).
thf(12136,plain,
( ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk21 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12130]) ).
thf(7518,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6734]) ).
thf(7519,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7518:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( B @ v2_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[169]) ).
thf(217,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)],[216]) ).
thf(219,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)],[217]) ).
thf(995,plain,
! [A: $i] :
( ( A != sk13 )
| ( k1_xboole_0 @ v3_yellow18 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,261]) ).
thf(996,plain,
( ( k1_xboole_0 @ v3_yellow18 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[995:[bind(A,$thf( sk13 ))]]) ).
thf(14662,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6723,147]) ).
thf(14663,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[14662]) ).
thf(14664,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[14663:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(362,plain,
! [A: $i] :
( ( A @ v1_membered )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(94,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(567,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)],[94]) ).
thf(13586,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(paramod_ordered,[status(thm)],[6667,147]) ).
thf(13587,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(simp,[status(thm)],[13586]) ).
thf(13588,plain,
( ( sk5 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_altcat_2 ) ),
inference(pattern_uni,[status(thm)],[13587:[bind(A,$thf( sk5 @ k5_waybel34 ))]]) ).
thf(1133,plain,
( ( ( sk6 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,855]) ).
thf(1134,plain,
( ( ( sk6 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1133]) ).
thf(1144,plain,
( ( sk6 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1134]) ).
thf(599,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v2_yellow18 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(635,plain,
sk29 @ v2_lattice3,
inference(cnfConj,[status(thm)],[624]) ).
thf(2282,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,635]) ).
thf(2283,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2282:[bind(A,$thf( sk29 ))]]) ).
thf(5612,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2283]) ).
thf(5613,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[5612]) ).
thf(5616,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[5613]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(494,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(353,plain,
sk16 @ v1_relat_1,
inference(cnfConj,[status(thm)],[352]) ).
thf(2610,plain,
k1_xboole_0 @ v1_relat_1,
inference(rewrite,[status(thm)],[353,1034]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[339]) ).
thf(609,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v1_altcat_2 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(140,plain,
( ~ sk3
| ( sk1 @ k9_waybel34 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(21,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(213,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3294,plain,
( ( ( sk12 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,922]) ).
thf(3295,plain,
( ( ( sk12 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3294]) ).
thf(3298,plain,
( ( sk12 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3295]) ).
thf(626,plain,
sk29 @ v3_yellow_0,
inference(cnfConj,[status(thm)],[624]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xcmplx_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(769,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( B @ v1_funct_1 )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[388]) ).
thf(18344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_funct_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,390]) ).
thf(18345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_funct_1 ) ),
inference(simp,[status(thm)],[18344]) ).
thf(18346,plain,
! [A: $i] : ( A @ sk14 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[18345:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk14 ))]]) ).
thf(18354,plain,
! [A: $i] : ( A @ sk14 @ v1_funct_1 ),
inference(simp,[status(thm)],[18346]) ).
thf(5171,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2064]) ).
thf(5172,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[5171]) ).
thf(5175,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[5172]) ).
thf(323,plain,
! [A: $i] :
( ( A @ v4_yellow18 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(6676,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1743]) ).
thf(6677,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6676]) ).
thf(6678,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6677:[bind(A,$thf( sk21 ))]]) ).
thf(2995,plain,
( ( ( sk5 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,865]) ).
thf(2996,plain,
( ( ( sk5 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[2995]) ).
thf(3006,plain,
( ( sk5 != k1_xboole_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[2996]) ).
thf(70,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(462,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)],[70]) ).
thf(6587,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v25_waybel_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2203]) ).
thf(6588,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v25_waybel_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6587]) ).
thf(6589,plain,
( ( k1_xboole_0 @ v25_waybel_0 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6588:[bind(A,$thf( sk29 ))]]) ).
thf(6685,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2283]) ).
thf(6686,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6685]) ).
thf(6687,plain,
( ( k1_xboole_0 @ v2_lattice3 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6686:[bind(A,$thf( sk29 ))]]) ).
thf(17702,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,7519]) ).
thf(17703,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[17702]) ).
thf(17708,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[17703]) ).
thf(6511,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,1115]) ).
thf(6512,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk21 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6511]) ).
thf(6513,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( sk21 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6512:[bind(A,$thf( sk21 ))]]) ).
thf(9247,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6513,147]) ).
thf(9248,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[9247]) ).
thf(9249,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[9248:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(866,plain,
! [A: $i] :
( ( A != sk13 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,257]) ).
thf(867,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk13 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( sk13 ))]]) ).
thf(1765,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,867]) ).
thf(1766,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1765]) ).
thf(1775,plain,
( ( sk13 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[1766]) ).
thf(226,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v2_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_altcat_1 @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_altcat_1) ).
thf(431,plain,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_altcat_1 @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(9749,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6528,147]) ).
thf(9750,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[9749]) ).
thf(9751,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[9750:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(118,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(695,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)],[118]) ).
thf(2474,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,831]) ).
thf(2475,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3 ),
inference(simp,[status(thm)],[2474]) ).
thf(2481,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_orders_2 )
| sk3 ),
inference(simp,[status(thm)],[2475]) ).
thf(6502,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow21 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,934]) ).
thf(6503,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow21 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6502]) ).
thf(6504,plain,
( ( k1_xboole_0 @ v3_yellow21 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6503:[bind(A,$thf( sk13 ))]]) ).
thf(223,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v11_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(608,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v1_yellow21 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(4823,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1883]) ).
thf(4824,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[4823]) ).
thf(4827,plain,
( ( sk23 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[4824]) ).
thf(14285,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6708,147]) ).
thf(14286,plain,
! [A: $i] :
( ( ( sk5 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(simp,[status(thm)],[14285]) ).
thf(14287,plain,
( ( sk5 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l2_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[14286:[bind(A,$thf( sk5 @ k5_waybel34 ))]]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(299,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[266]) ).
thf(4622,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1752]) ).
thf(4623,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[4622]) ).
thf(4626,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[4623]) ).
thf(238,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[237]) ).
thf(241,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
| ( A = D )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(14941,plain,
( ( ( sk17 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6909]) ).
thf(14942,plain,
( ( ( sk17 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14941]) ).
thf(14947,plain,
( ( ( sk17 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14942]) ).
thf(4961,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1988]) ).
thf(4962,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4961]) ).
thf(4965,plain,
( ( sk23 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4962]) ).
thf(5657,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2309]) ).
thf(5658,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[5657]) ).
thf(5661,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[5658]) ).
thf(77,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(490,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)],[77]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( B @ v1_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(7488,plain,
( ~ $true
| ( ( sk19 @ k5_waybel34 @ l1_altcat_1 )
!= ( k1_xboole_0 @ l1_altcat_1 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(eqfactor_ordered,[status(thm)],[6480]) ).
thf(7490,plain,
( ( ( sk19 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7488]) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_1 )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ l1_orders_2 )
| ~ ( B @ v2_lattice3 )
| ~ ( B @ v1_lattice3 )
| ~ ( B @ v4_orders_2 )
| ~ ( B @ v3_orders_2 )
| ~ ( B @ v2_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ v4_orders_2 )
| ~ ( A @ v3_orders_2 )
| ~ ( A @ v2_orders_2 ) ),
inference(cnfConj,[status(thm)],[425]) ).
thf(6538,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2508]) ).
thf(6539,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_yellow_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6538]) ).
thf(6540,plain,
( ( k1_xboole_0 @ v1_yellow_0 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6539:[bind(A,$thf( sk31 ))]]) ).
thf(130,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(795,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(115,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(680,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)],[115]) ).
thf(4452,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1119]) ).
thf(4453,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[4452]) ).
thf(4456,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[4453]) ).
thf(14235,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10536]) ).
thf(14236,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[14235]) ).
thf(14250,plain,
( ( sk29 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[14236]) ).
thf(91,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(548,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)],[91]) ).
thf(11016,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,829]) ).
thf(11017,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11016]) ).
thf(11030,plain,
( ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11017]) ).
thf(810,plain,
( ( ( sk17 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,386]) ).
thf(811,plain,
( ( sk17 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[810]) ).
thf(812,plain,
sk17 != k1_xboole_0,
inference(simp,[status(thm)],[811]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ! [B: $i] :
( ( B @ l2_altcat_1 )
=> ( ( A @ ( B @ m1_altcat_2 ) )
<=> ( ( A @ u2_altcat_1 @ ( B @ u2_altcat_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_zfmisc_1 ) ) @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_zfmisc_1 ) ) @ r2_altcat_2 ) ) ) )
& ( A @ u1_altcat_1 @ ( B @ u1_altcat_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ r2_altcat_2 ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_altcat_2) ).
thf(617,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ! [B: $i] :
( ( B @ l2_altcat_1 )
=> ( ( ( ( A @ u2_altcat_1 @ ( B @ u2_altcat_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_zfmisc_1 ) ) @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_zfmisc_1 ) ) @ r2_altcat_2 ) ) ) )
& ( A @ u1_altcat_1 @ ( B @ u1_altcat_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ r2_altcat_2 ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
=> ( A @ ( B @ m1_altcat_2 ) ) )
& ( ( A @ ( B @ m1_altcat_2 ) )
=> ( ( A @ u2_altcat_1 @ ( B @ u2_altcat_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_zfmisc_1 ) ) @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_zfmisc_1 ) ) @ r2_altcat_2 ) ) ) )
& ( A @ u1_altcat_1 @ ( B @ u1_altcat_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ r2_altcat_2 ) ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(83,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(516,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)],[83]) ).
thf(86,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(525,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)],[86]) ).
thf(121,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(712,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)],[121]) ).
thf(117,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(690,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)],[117]) ).
thf(1066,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,912]) ).
thf(1067,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[1066]) ).
thf(1070,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[1067]) ).
thf(13489,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6655,147]) ).
thf(13490,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[13489]) ).
thf(13491,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(pattern_uni,[status(thm)],[13490:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(952,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,861]) ).
thf(953,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[952]) ).
thf(954,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[953]) ).
thf(2576,plain,
( ( ( sk16 @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,926]) ).
thf(2577,plain,
( ( ( sk16 @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3 ),
inference(simp,[status(thm)],[2576]) ).
thf(2578,plain,
( ( sk16 != sk2 )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3 ),
inference(simp,[status(thm)],[2577]) ).
thf(2678,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3 ),
inference(rewrite,[status(thm)],[2578,1034]) ).
thf(408,plain,
! [A: $i] :
( ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v4_orders_2 ) )
& ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v4_orders_2 ) ) ),
inference(cnf,[status(esa)],[407]) ).
thf(409,plain,
! [A: $i] :
( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v4_orders_2 ) ),
inference(cnfConj,[status(thm)],[408]) ).
thf(13779,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10528]) ).
thf(13780,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13779]) ).
thf(13793,plain,
( ( sk2 != k1_xboole_0 )
| ( sk29 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13780]) ).
thf(18139,plain,
! [A: $i] :
( ( A != sk29 )
| ( sk2 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,13793]) ).
thf(18140,plain,
! [A: $i] :
( ( A != sk29 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[18139]) ).
thf(18141,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18140:[bind(A,$thf( sk29 ))]]) ).
thf(6575,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2515]) ).
thf(6576,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk31 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6575]) ).
thf(6577,plain,
( ( k1_xboole_0 @ v3_yellow_0 )
| ( sk31 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6576:[bind(A,$thf( sk31 ))]]) ).
thf(18335,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,7683]) ).
thf(18336,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[18335]) ).
thf(18341,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[18336]) ).
thf(25698,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ u1_struct_0 @ v1_xboole_0 ) )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,25631]) ).
thf(25699,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ u1_struct_0 @ v1_xboole_0 ) )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[25698]) ).
thf(25700,plain,
sk29 @ u1_struct_0 @ k5_waybel34 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[25699:[bind(A,$thf( sk29 @ u1_struct_0 ))]]) ).
thf(2382,plain,
( ( ( sk31 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true
| ~ ( sk2 @ v1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[658,135]) ).
thf(2383,plain,
( ( ( sk31 @ v3_lattice3 )
!= ( sk2 @ v3_lattice3 ) )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[2382]) ).
thf(2386,plain,
( ( sk31 != sk2 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[2383]) ).
thf(6028,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2515]) ).
thf(6029,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 ) ),
inference(simp,[status(thm)],[6028]) ).
thf(6036,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_yellow_0 ) ),
inference(simp,[status(thm)],[6029]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( B @ v3_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(5991,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2501]) ).
thf(5992,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[5991]) ).
thf(5995,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[5992]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( A @ v6_altcat_1 )
=> ( A
= ( A @ u2_altcat_1 @ ( A @ u1_altcat_1 @ ( A @ u1_struct_0 @ g2_altcat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v6_altcat_1) ).
thf(576,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( A @ v6_altcat_1 )
=> ( A
= ( A @ u2_altcat_1 @ ( A @ u1_altcat_1 @ ( A @ u1_struct_0 @ g2_altcat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(359,plain,
! [A: $i] :
( ( A @ v2_membered )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(22150,plain,
( ( ( sk13 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,22136]) ).
thf(22151,plain,
( ( sk13 @ u1_struct_0 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[22150]) ).
thf(22156,plain,
( ( sk13 @ u1_struct_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[22151]) ).
thf(11,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(177,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(182,plain,
! [A: $i] :
( ( A @ v3_membered )
| ~ ( A @ v4_membered ) ),
inference(cnf,[status(esa)],[181]) ).
thf(6170,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2522]) ).
thf(6171,plain,
( ( ( sk31 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[6170]) ).
thf(6174,plain,
( ( sk31 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[6171]) ).
thf(7748,plain,
( ( ( sk11 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,3504]) ).
thf(7749,plain,
( ( ( sk11 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[7748]) ).
thf(7752,plain,
( ( sk11 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[7749]) ).
thf(335,plain,
( ( sk15 @ v1_funct_1 )
& ( sk15 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[334]) ).
thf(336,plain,
sk15 @ v1_relat_1,
inference(cnfConj,[status(thm)],[335]) ).
thf(1058,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,908]) ).
thf(1059,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1062,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[1059]) ).
thf(25594,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( sk2 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1062,430]) ).
thf(25595,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[25594]) ).
thf(25596,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk2 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25595:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(17714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10741,389]) ).
thf(17715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_relat_1 ) ),
inference(simp,[status(thm)],[17714]) ).
thf(17716,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[17715:[bind(A,$thf( K )),bind(B,$thf( K @ ( K @ ( K @ k3_zfmisc_1 ) ) )),bind(C,$thf( K @ ( K @ k2_zfmisc_1 ) @ sk14 @ ( K @ k2_altcat_1 ) ))]]) ).
thf(17721,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[17716]) ).
thf(6620,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow18 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,996]) ).
thf(6621,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow18 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6620]) ).
thf(6622,plain,
( ( k1_xboole_0 @ v3_yellow18 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6621:[bind(A,$thf( sk13 ))]]) ).
thf(7617,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,3386]) ).
thf(7618,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7617]) ).
thf(7621,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7618]) ).
thf(600,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v3_yellow21 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B @ v11_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[169]) ).
thf(6529,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2002]) ).
thf(6530,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6529]) ).
thf(6531,plain,
( ( k1_xboole_0 @ l1_orders_2 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6530:[bind(A,$thf( sk29 ))]]) ).
thf(7657,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6483,147]) ).
thf(7658,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(simp,[status(thm)],[7657]) ).
thf(7659,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[7658:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(6709,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,867]) ).
thf(6710,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk13 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6709]) ).
thf(6711,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk13 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6710:[bind(A,$thf( sk13 ))]]) ).
thf(14584,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6711,147]) ).
thf(14585,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[14584]) ).
thf(14586,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[14585:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(214,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk10 ) @ m1_relset_1 ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[155]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(2787,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk10 ) @ m1_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m1_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,158]) ).
thf(2788,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk10 ) @ m1_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m1_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[2787]) ).
thf(2789,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk10 ) @ m2_relset_1 ) ) ),
inference(pattern_uni,[status(thm)],[2788:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk10 ) ))]]) ).
thf(2792,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk10 ) @ m2_relset_1 ) ) ),
inference(simp,[status(thm)],[2789]) ).
thf(2811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk10 ) @ m2_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m2_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m1_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2792,156]) ).
thf(2812,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk10 ) @ m2_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m2_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m1_relset_1 ) ) ) ),
inference(simp,[status(thm)],[2811]) ).
thf(2813,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk10 ) @ m1_relset_1 ) ) ),
inference(pattern_uni,[status(thm)],[2812:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk10 ) ))]]) ).
thf(2818,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk10 ) @ m1_relset_1 ) ) ),
inference(simp,[status(thm)],[2813]) ).
thf(3167,plain,
( ( ( sk6 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,899]) ).
thf(3168,plain,
( ( ( sk6 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3167]) ).
thf(3171,plain,
( ( sk6 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[3168]) ).
thf(10031,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6531,147]) ).
thf(10032,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[10031]) ).
thf(10033,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(pattern_uni,[status(thm)],[10032:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(18347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_funct_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10741,390]) ).
thf(18348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ m1_pboole ) )
!= ( B @ ( C @ m1_pboole ) ) )
| ( C @ v1_funct_1 ) ),
inference(simp,[status(thm)],[18347]) ).
thf(18349,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[18348:[bind(A,$thf( K )),bind(B,$thf( K @ ( K @ ( K @ k3_zfmisc_1 ) ) )),bind(C,$thf( K @ ( K @ k2_zfmisc_1 ) @ sk14 @ ( K @ k2_altcat_1 ) ))]]) ).
thf(18355,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ sk14 @ ( A @ k2_altcat_1 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[18349]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( B @ v9_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(482,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ m3_pboole ) ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[202]) ).
thf(1008,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,877]) ).
thf(1009,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1010,plain,
( ( sk1 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[1009]) ).
thf(126,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(771,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)],[126]) ).
thf(119,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(699,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)],[119]) ).
thf(4464,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1146]) ).
thf(4465,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[4464]) ).
thf(4468,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_orders_2 ) ),
inference(simp,[status(thm)],[4465]) ).
thf(13719,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6687,147]) ).
thf(13720,plain,
! [A: $i] :
( ( ( sk29 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[13719]) ).
thf(13721,plain,
( ( sk29 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(pattern_uni,[status(thm)],[13720:[bind(A,$thf( sk29 @ k5_waybel34 ))]]) ).
thf(6593,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,926]) ).
thf(6594,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk2 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6593]) ).
thf(6595,plain,
( ( k1_xboole_0 @ v3_lattice3 )
| sk3
| ( sk2 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6594:[bind(A,$thf( sk2 ))]]) ).
thf(10048,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_lattice3 )
| sk3 ),
inference(paramod_ordered,[status(thm)],[6595,147]) ).
thf(10049,plain,
! [A: $i] :
( ( ( sk2 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3 ),
inference(simp,[status(thm)],[10048]) ).
thf(10050,plain,
( ( sk2 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_lattice3 )
| sk3 ),
inference(pattern_uni,[status(thm)],[10049:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(110,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(652,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)],[110]) ).
thf(4787,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1856]) ).
thf(4788,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[4787]) ).
thf(4791,plain,
( ( sk23 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_orders_2 ) ),
inference(simp,[status(thm)],[4788]) ).
thf(2008,plain,
! [A: $i] :
( ( A != sk29 )
| ( k1_xboole_0 @ v3_yellow_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,626]) ).
thf(2009,plain,
( ( k1_xboole_0 @ v3_yellow_0 )
| ~ ( sk29 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2008:[bind(A,$thf( sk29 ))]]) ).
thf(4598,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1736]) ).
thf(4599,plain,
( ( ( sk21 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[4598]) ).
thf(4602,plain,
( ( sk21 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_lattice3 ) ),
inference(simp,[status(thm)],[4599]) ).
thf(25588,plain,
! [A: $i] :
( ( ( sk25 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[502,430]) ).
thf(25589,plain,
! [A: $i] :
( ( ( sk25 @ l1_orders_2 )
!= ( A @ l1_orders_2 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[25588]) ).
thf(25590,plain,
sk25 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[25589:[bind(A,$thf( sk25 ))]]) ).
thf(207,plain,
sk8 @ v1_funct_1,
inference(cnfConj,[status(thm)],[205]) ).
thf(178,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk4 ) @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[177]) ).
thf(2487,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk4 ) @ m2_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m2_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m1_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,156]) ).
thf(2488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk4 ) @ m2_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m2_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m1_relset_1 ) ) ) ),
inference(simp,[status(thm)],[2487]) ).
thf(2489,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk4 ) @ m1_relset_1 ) ) ),
inference(pattern_uni,[status(thm)],[2488:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(2494,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk4 ) @ m1_relset_1 ) ) ),
inference(simp,[status(thm)],[2489]) ).
thf(13667,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(paramod_ordered,[status(thm)],[6670,147]) ).
thf(13668,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[13667]) ).
thf(13669,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(pattern_uni,[status(thm)],[13668:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(6194,plain,
( ( ( sk19 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2635]) ).
thf(6195,plain,
( ( ( sk19 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[6194]) ).
thf(6198,plain,
( ( sk19 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[6195]) ).
thf(5154,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2009]) ).
thf(5155,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 ) ),
inference(simp,[status(thm)],[5154]) ).
thf(5162,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_yellow_0 ) ),
inference(simp,[status(thm)],[5155]) ).
thf(245,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_altcat_2 ) ) ),
inference(miniscope,[status(thm)],[244]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ r1_altcat_2 ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[245]) ).
thf(82,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [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 @ k5_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
<=> ( ( A @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_waybel34) ).
thf(510,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ! [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 @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) )
=> ( A @ k5_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
& ( ( A @ k5_waybel34 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ u1_struct_0 @ r2_hidden ) )
& ( B @ v3_lattice3 )
& ( B @ v1_orders_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(478,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(763,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(383,plain,
sk17 @ v3_membered,
inference(cnfConj,[status(thm)],[380]) ).
thf(16025,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk21 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,12133]) ).
thf(16026,plain,
( ( sk21 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16025:[bind(A,$thf( sk2 ))]]) ).
thf(16038,plain,
( ( sk21 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( k1_xboole_0 @ u1_struct_0 @ r2_hidden ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16026]) ).
thf(300,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(cnf,[status(esa)],[299]) ).
thf(444,plain,
! [A: $i] :
( ( ( A @ sk22 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk22 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk22 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[443]) ).
thf(447,plain,
! [A: $i] :
( ( A @ sk22 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[444]) ).
thf(3979,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow18 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,996]) ).
thf(3980,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow18 ) ),
inference(simp,[status(thm)],[3979]) ).
thf(3987,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_yellow18 ) ),
inference(simp,[status(thm)],[3980]) ).
thf(13301,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,10201]) ).
thf(13302,plain,
( ( ( sk23 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13301]) ).
thf(13314,plain,
( ( sk23 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ u1_struct_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13302]) ).
thf(6760,plain,
! [A: $i] :
( ( A
!= ( sk2 @ k5_waybel34 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,6507]) ).
thf(6761,plain,
( ( k1_xboole_0 @ v1_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk2 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6760:[bind(A,$thf( sk2 @ k5_waybel34 ))]]) ).
thf(14978,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6761]) ).
thf(14979,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v1_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14978]) ).
thf(14984,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ v1_lattice3 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14979]) ).
thf(5183,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2139]) ).
thf(5184,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[5183]) ).
thf(5187,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_lattice3 ) ),
inference(simp,[status(thm)],[5184]) ).
thf(6691,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2009]) ).
thf(6692,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_yellow_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6691]) ).
thf(6693,plain,
( ( k1_xboole_0 @ v3_yellow_0 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6692:[bind(A,$thf( sk29 ))]]) ).
thf(432,plain,
! [A: $i] :
( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_altcat_1 @ m1_pboole ) )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnf,[status(esa)],[431]) ).
thf(410,plain,
! [A: $i] :
( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v4_orders_2 ) ),
inference(cnfConj,[status(thm)],[408]) ).
thf(25670,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,25587]) ).
thf(25671,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25670:[bind(A,$thf( sk2 ))]]) ).
thf(190,plain,
k1_xboole_0 @ v1_membered,
inference(cnfConj,[status(thm)],[189]) ).
thf(15656,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[7610,147]) ).
thf(15657,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[15656]) ).
thf(15658,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[15657:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(13693,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6678,147]) ).
thf(13694,plain,
! [A: $i] :
( ( ( sk21 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[13693]) ).
thf(13695,plain,
( ( sk21 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(pattern_uni,[status(thm)],[13694:[bind(A,$thf( sk21 @ k5_waybel34 ))]]) ).
thf(129,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(790,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)],[129]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( B @ v3_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[266]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( B @ v4_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(603,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v2_yellow21 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(302,plain,
! [A: $i] :
( ( ( A @ v2_funct_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ v1_funct_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[301]) ).
thf(305,plain,
! [A: $i] :
( ( A @ v2_funct_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[302]) ).
thf(239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[237]) ).
thf(242,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ g2_altcat_1 ) ) )
!= ( F @ ( E @ ( D @ g2_altcat_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v1_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[339]) ).
thf(14918,plain,
( ( ( sk9 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,6892]) ).
thf(14919,plain,
( ( ( sk9 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14918]) ).
thf(14924,plain,
( ( ( sk9 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[14919]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( B @ v12_altcat_1 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow18 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[266]) ).
thf(358,plain,
! [A: $i] :
( ( A @ v5_membered )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(195,plain,
k1_xboole_0 @ v4_membered,
inference(cnfConj,[status(thm)],[189]) ).
thf(19850,plain,
! [A: $i] :
( ( ( sk5 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ ( A @ sk18 @ m1_altcat_2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[185,400]) ).
thf(19851,plain,
! [A: $i] :
( ( ( sk5 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ ( A @ sk18 @ m1_altcat_2 ) ) ),
inference(simp,[status(thm)],[19850]) ).
thf(19852,plain,
sk5 @ ( sk5 @ sk18 @ m1_altcat_2 ),
inference(pattern_uni,[status(thm)],[19851:[bind(A,$thf( sk5 ))]]) ).
thf(7472,plain,
! [A: $i] :
( ( ( sk19 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6480,147]) ).
thf(7473,plain,
! [A: $i] :
( ( ( sk19 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[7472]) ).
thf(7474,plain,
( ( sk19 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[7473:[bind(A,$thf( sk19 @ k5_waybel34 ))]]) ).
thf(6535,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v24_waybel_0 )
| ~ $true
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[3367,2154]) ).
thf(6536,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk29 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v24_waybel_0 )
| ( A @ k5_waybel34 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[6535]) ).
thf(6537,plain,
( ( k1_xboole_0 @ v24_waybel_0 )
| ( sk29 @ k5_waybel34 @ l1_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[6536:[bind(A,$thf( sk29 ))]]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( B @ v1_yellow21 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( B @ v9_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v9_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[392]) ).
thf(3233,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow18 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,914]) ).
thf(3234,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_yellow18 ) ),
inference(simp,[status(thm)],[3233]) ).
thf(3244,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_yellow18 ) ),
inference(simp,[status(thm)],[3234]) ).
thf(12000,plain,
! [A: $i] :
( ( ( sk26 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(paramod_ordered,[status(thm)],[6495,147]) ).
thf(12001,plain,
! [A: $i] :
( ( ( sk26 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[12000]) ).
thf(12002,plain,
( ( sk26 @ k5_waybel34 @ l1_struct_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(pattern_uni,[status(thm)],[12001:[bind(A,$thf( sk26 @ k5_waybel34 ))]]) ).
thf(14125,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(paramod_ordered,[status(thm)],[6705,147]) ).
thf(14126,plain,
! [A: $i] :
( ( ( sk31 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(simp,[status(thm)],[14125]) ).
thf(14127,plain,
( ( sk31 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v1_lattice3 ) ),
inference(pattern_uni,[status(thm)],[14126:[bind(A,$thf( sk31 @ k5_waybel34 ))]]) ).
thf(427,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_waybel34 ) ) @ v1_funct_2 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ l1_orders_2 )
| ~ ( B @ v2_lattice3 )
| ~ ( B @ v1_lattice3 )
| ~ ( B @ v4_orders_2 )
| ~ ( B @ v3_orders_2 )
| ~ ( B @ v2_orders_2 )
| ~ ( A @ l1_orders_2 )
| ~ ( A @ v2_lattice3 )
| ~ ( A @ v1_lattice3 )
| ~ ( A @ v4_orders_2 )
| ~ ( A @ v3_orders_2 )
| ~ ( A @ v2_orders_2 ) ),
inference(cnfConj,[status(thm)],[425]) ).
thf(2800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk4 ) @ m1_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m1_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2494,158]) ).
thf(2801,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk4 ) @ m1_relset_1 ) ) )
!= ( D @ ( C @ ( E @ m1_relset_1 ) ) ) )
| ( D @ ( C @ ( E @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[2800]) ).
thf(2802,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk4 ) @ m2_relset_1 ) ) ),
inference(pattern_uni,[status(thm)],[2801:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(2803,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk4 ) @ m2_relset_1 ) ) ),
inference(simp,[status(thm)],[2802]) ).
thf(6381,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true
| ( sk5 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[3006,233]) ).
thf(6382,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ( sk5 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6381]) ).
thf(6383,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ( sk5 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6382:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( B @ v2_yellow18 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v3_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(3527,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v11_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,932]) ).
thf(3528,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v11_altcat_1 ) ),
inference(simp,[status(thm)],[3527]) ).
thf(3538,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v11_altcat_1 ) ),
inference(simp,[status(thm)],[3528]) ).
thf(13159,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ v11_altcat_1 ) ),
inference(paramod_ordered,[status(thm)],[6631,147]) ).
thf(13160,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ v11_altcat_1 ) ),
inference(simp,[status(thm)],[13159]) ).
thf(13161,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ v11_altcat_1 ) ),
inference(pattern_uni,[status(thm)],[13160:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ v1_altcat_2 )
| ~ ( A @ ( B @ v3_altcat_2 ) )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ ( B @ m1_altcat_2 ) )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(607,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v9_altcat_1 )
| ( A @ v2_setfam_1 ) ),
inference(cnfConj,[status(thm)],[596]) ).
thf(17463,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,7505]) ).
thf(17464,plain,
( ( ( sk2 @ k5_waybel34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[17463]) ).
thf(17469,plain,
( ( ( sk2 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 )
| ( k1_xboole_0 @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[17464]) ).
thf(3890,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v12_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,984]) ).
thf(3891,plain,
( ( ( sk13 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v12_altcat_1 ) ),
inference(simp,[status(thm)],[3890]) ).
thf(3901,plain,
( ( sk13 != k1_xboole_0 )
| ( k1_xboole_0 @ v12_altcat_1 ) ),
inference(simp,[status(thm)],[3891]) ).
thf(322,plain,
! [A: $i] :
( ( A @ v9_altcat_1 )
| ~ ( A @ v2_yellow21 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(337,plain,
sk15 @ v1_funct_1,
inference(cnfConj,[status(thm)],[335]) ).
thf(5645,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,2297]) ).
thf(5646,plain,
( ( ( sk29 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[5645]) ).
thf(5649,plain,
( ( sk29 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_orders_2 ) ),
inference(simp,[status(thm)],[5646]) ).
thf(4973,plain,
( ( ( sk25 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[194,1995]) ).
thf(4974,plain,
( ( ( sk25 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4973]) ).
thf(4977,plain,
( ( sk25 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_orders_2 ) ),
inference(simp,[status(thm)],[4974]) ).
thf(227,plain,
! [A: $i] :
( ( A @ k5_waybel34 @ v6_altcat_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[222]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ g2_altcat_1 ) ) @ l2_altcat_1 )
| ~ ( B @ ( A @ k2_altcat_1 ) @ ( B @ ( B @ ( A @ k3_altcat_1 ) ) @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m3_pboole ) ) ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[307]) ).
thf(16657,plain,
( ~ $true
| ( ( sk19 @ k5_waybel34 @ l1_struct_0 )
!= ( k1_xboole_0 @ l1_struct_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(eqfactor_ordered,[status(thm)],[9447]) ).
thf(16659,plain,
( ( ( sk19 @ k5_waybel34 )
!= k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16657]) ).
thf(107,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(639,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)],[107]) ).
thf(16652,plain,
! [A: $i] :
( ( A
!= ( sk19 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[150,9447]) ).
thf(16653,plain,
! [A: $i] :
( ( A
!= ( sk19 @ k5_waybel34 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16652]) ).
thf(16654,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk19 @ k5_waybel34 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16653:[bind(A,$thf( sk19 @ k5_waybel34 ))]]) ).
thf(79,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(496,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)],[79]) ).
thf(15897,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7640,147]) ).
thf(15898,plain,
! [A: $i] :
( ( ( sk13 @ k5_waybel34 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15897]) ).
thf(15899,plain,
( ( sk13 @ k5_waybel34 @ l1_struct_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(pattern_uni,[status(thm)],[15898:[bind(A,$thf( sk13 @ k5_waybel34 ))]]) ).
thf(32284,plain,
$false,
inference(e,[status(thm)],[7304,809,3962,629,4101,2031,1995,518,234,6690,555,666,1110,25695,645,365,138,347,1729,249,333,628,16898,2309,15547,16086,683,276,6495,6744,1808,6619,308,13424,379,4614,269,7208,6480,861,247,15568,202,597,13660,385,384,3429,3367,142,14726,6634,1988,5636,6640,6655,4638,14084,18536,538,153,185,10230,1001,17492,6909,417,885,4803,436,257,829,3370,174,1095,404,6583,288,3281,25457,301,15295,16979,14612,2400,10530,6483,389,9447,15674,6892,6552,14690,785,7683,6723,587,344,934,6519,196,460,19895,2501,949,6643,3713,15182,817,638,6681,12291,421,606,284,416,11827,289,448,26160,1875,6734,261,10025,11264,5199,1115,2635,325,25717,6923,152,3734,228,1847,9712,179,443,321,376,623,6534,4815,480,6670,591,211,646,253,348,3357,10201,6717,147,397,6631,280,634,877,221,5370,9743,453,1119,6498,396,133,2002,428,12133,6616,2154,206,6474,602,2508,660,6702,411,988,25587,243,7505,265,9048,7321,2922,292,233,920,3301,678,4480,201,6684,10197,381,6571,13519,1736,15873,942,4323,13848,529,6015,661,220,366,12073,15542,6652,334,22136,12385,4989,2147,6565,424,137,165,17599,1883,825,7703,260,349,12550,6528,561,16465,297,15531,192,407,630,429,7640,15563,6696,5983,361,13562,625,3403,7625,1027,2741,456,324,1012,224,916,6646,229,5391,484,252,10634,25649,435,7314,3137,25495,13536,329,6708,13070,665,583,522,26130,889,8181,10067,461,757,3926,12863,2515,7962,6477,1856,403,3386,356,5811,593,610,420,156,615,188,7610,141,869,15669,6720,5337,14110,10195,6501,212,328,256,488,12768,225,12906,193,537,10528,669,6661,12639,476,637,14189,6946,4444,6625,25566,7976,7651,17720,1131,457,569,3692,6186,8219,25678,3354,6999,9739,7485,984,3390,7495,10588,4953,371,12831,503,605,134,3755,244,2203,3563,508,6592,12923,398,15552,6610,9744,22177,773,926,343,15349,938,6963,19332,360,633,8205,6486,12889,3173,11524,662,718,298,6637,14638,166,25669,148,264,161,279,7636,6492,6598,6507,26214,12168,1146,13041,430,14045,19963,14254,6699,6546,180,3158,601,819,3504,11836,5844,12317,7440,5831,5350,413,176,7287,7938,423,191,1916,402,12986,6510,2393,286,1752,8697,12840,579,5799,281,204,259,6705,391,936,382,6667,144,1865,13380,11515,2055,181,704,6549,10741,10505,641,2161,16043,313,6937,7455,236,15205,350,540,7741,13385,6525,159,672,604,187,25474,406,274,419,509,12136,6604,208,863,7519,172,10532,831,6613,219,377,996,230,14664,362,567,13588,1144,599,5616,387,494,2610,345,535,609,140,213,251,3298,626,769,668,330,18354,631,6989,5175,323,6678,3006,6568,198,462,932,912,6589,6574,6687,827,17708,9249,2064,1775,226,431,658,3380,399,9751,636,695,2481,6628,9741,2139,455,6504,223,608,4827,986,306,135,1113,14287,3363,299,267,4626,241,14947,922,167,4965,5661,1034,490,374,25560,2564,6664,7490,6977,426,6540,162,944,795,680,4456,663,14250,548,255,6751,11030,209,2449,812,617,516,458,823,194,145,525,712,690,1070,13491,282,887,414,954,2678,25610,409,18141,6577,25454,855,150,1743,18341,25700,2407,2386,263,310,199,6036,331,370,502,6513,2276,5995,576,359,22156,177,182,338,6174,7752,336,6899,656,6601,25596,13374,314,595,3366,17721,6622,10536,7331,7621,600,175,386,143,6531,7659,14586,627,2818,363,10526,3171,10033,10199,18355,368,250,231,482,203,1010,6882,6543,2792,771,6711,6726,699,2283,6607,4468,1062,258,390,632,401,13441,139,13721,418,25602,10050,6489,2290,25575,158,652,351,4791,186,2009,6516,4602,25590,207,667,899,11772,2494,13669,6198,13793,914,378,5162,235,246,433,510,478,22139,6586,763,3351,383,214,16038,300,25631,447,2385,146,3987,13314,2522,405,14984,865,6580,5187,151,6693,432,410,25671,168,262,190,15658,13695,183,422,790,867,273,373,603,10205,305,326,242,341,14924,268,358,195,6714,400,19852,635,415,918,136,7474,664,6537,283,395,3244,12002,332,14127,427,2803,6383,459,131,200,178,277,908,9737,6595,3538,982,13161,501,6658,369,607,17469,3901,322,337,940,5649,215,2297,4977,232,254,227,309,659,16659,639,16654,6761,496,15899]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT374+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
% 0.13/5.40 % Computer : n016.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Fri Sep 25 21:36:35 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 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
% 0.17/5.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/6.25 % [INFO] Parsing done (264ms).
% 1.39/6.26 % [INFO] Running in sequential loop mode.
% 2.32/6.65 % [INFO] eprover registered as external prover.
% 2.32/6.66 % [INFO] Scanning for conjecture ...
% 2.72/6.80 % [INFO] Found a conjecture (or negated_conjecture) and 137 axioms. Running axiom selection ...
% 2.99/6.93 % [INFO] Axiom selection finished. Selected 128 axioms (removed 9 axioms).
% 3.44/7.09 % [INFO] Problem is first-order (TPTP FOF).
% 3.44/7.10 % [INFO] Type checking passed.
% 3.44/7.11 % [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 ...
% 101.25/30.44 % External prover 'e' found a proof!
% 101.25/30.44 % [INFO] Killing All external provers ...
% 101.25/30.44 % Time passed: 24893ms (effective reasoning time: 24173ms)
% 101.25/30.44 % 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)>
% 101.25/30.45 % Axioms used in derivation (128): rc2_yellow_0, dt_k3_altcat_1, cc15_membered, existence_l1_struct_0, rc2_setfam_1, redefinition_m2_relset_1, fc1_altcat_4, existence_m1_altcat_2, cc1_waybel17, cc2_finset_1, dt_l1_altcat_1, rc7_functor0, cc12_membered, dt_g2_altcat_1, rc4_finset_1, dt_k5_yellow21, redefinition_k3_yellow21, fc10_waybel_8, cc10_membered, dt_k9_waybel34, dt_u2_altcat_1, cc2_yellow21, t1_subset, rc1_membered, d11_altcat_2, d6_yellow21, rc1_waybel10, dt_l2_altcat_1, dt_m3_pboole, cc12_waybel_0, rc3_funct_1, cc1_lattice3, dt_m2_relset_1, cc11_waybel_0, rc13_waybel_0, cc14_waybel_0, d11_waybel34, rc1_funct_1, dt_u1_orders_2, cc5_yellow21, rc1_lattice3, fc8_waybel_8, fc6_waybel_8, dt_k1_yellow21, rc2_lattice3, t6_boole, fc6_waybel34, redefinition_r2_altcat_2, t5_subset, cc9_waybel_0, cc19_membered, cc8_yellow21, existence_m1_relset_1, rc3_setfam_1, fc7_waybel_8, cc7_yellow21, fc6_membered, existence_l2_altcat_1, cc11_membered, cc2_functor0, t4_subset, fc9_waybel_8, cc20_membered, t7_boole, existence_l1_orders_2, cc1_funct_1, dt_m1_altcat_2, rc3_struct_0, cc13_waybel_0, dt_g1_orders_2, rc2_funct_1, cc2_setfam_1, cc4_membered, cc1_yellow_2, dt_m1_pboole, existence_m3_pboole, cc18_membered, abstractness_v1_orders_2, cc4_yellow_0, existence_m1_pboole, cc2_funct_1, cc1_yellow21, t3_subset, cc1_relset_1, cc13_membered, existence_m1_subset_1, dt_k2_altcat_1, existence_m2_relset_1, existence_l1_altcat_1, free_g2_altcat_1, dt_l1_orders_2, free_g1_orders_2, fc1_struct_0, rc1_yellow21, dt_k5_waybel34, reflexivity_r1_tarski, cc11_yellow21, cc17_membered, cc9_yellow21, cc10_waybel_0, cc5_yellow_0, rc3_finset_1, dt_u1_altcat_1, rc1_finset_1, fc4_waybel_8, cc1_finset_1, dt_k3_yellow21, cc1_yellow_0, t8_boole, reflexivity_r2_altcat_2, rc5_struct_0, t2_subset, cc1_membered, abstractness_v6_altcat_1, cc2_membered, cc2_lattice3, cc3_membered, cc14_membered, cc6_yellow21, cc16_membered, reflexivity_r1_altcat_2, dt_k2_waybel34, fc14_finset_1, cc3_yellow_0, fc5_waybel_8, t15_waybel34, antisymmetry_r2_hidden, fc15_finset_1
% 101.25/30.45 % No. of inferences in proof: 1831
% 101.25/30.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24893 ms resp. 24173 ms w/o parsing
% 97.13/30.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 97.54/30.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------