%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT376+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 : n001.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 07:47:35 AM UTC 2026
% Result : Theorem 82.86s 19.45s
% Output : Refutation 83.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 83
% Syntax : Number of formulae : 279 ( 66 unt; 0 typ; 15 def)
% Number of atoms : 1476 ( 75 equ; 0 cnn)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 4176 ( 490 ~; 304 |; 634 &;2566 @)
% ( 0 <=>; 182 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 61 usr; 12 con; 0-5 aty)
% Number of variables : 389 ( 9 ^; 318 !; 47 ?; 389 :)
% ( 0 !>; 0 ?*; 0 @-; 15 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v2_setfam_1_decl,type,
v2_setfam_1: $i > $o ).
thf(r3_yellow20_decl,type,
r3_yellow20: $i > $i > $i > $i > $i > $o ).
thf(k5_waybel34_decl,type,
k5_waybel34: $i > $i ).
thf(k4_waybel34_decl,type,
k4_waybel34: $i > $i ).
thf(k7_waybel34_decl,type,
k7_waybel34: $i > $i ).
thf(k9_waybel34_decl,type,
k9_waybel34: $i > $i ).
thf(k8_waybel34_decl,type,
k8_waybel34: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(l1_altcat_1_decl,type,
l1_altcat_1: $i > $o ).
thf(l2_functor0_decl,type,
l2_functor0: $i > $i > $i > $o ).
thf(l1_functor0_decl,type,
l1_functor0: $i > $i > $i > $o ).
thf(v9_functor0_decl,type,
v9_functor0: $i > $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(l2_altcat_1_decl,type,
l2_altcat_1: $i > $o ).
thf(v11_functor0_decl,type,
v11_functor0: $i > $i > $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(v12_altcat_1_decl,type,
v12_altcat_1: $i > $o ).
thf(m2_functor0_decl,type,
m2_functor0: $i > $i > $i > $o ).
thf(v16_functor0_decl,type,
v16_functor0: $i > $i > $i > $o ).
thf(v6_functor0_decl,type,
v6_functor0: $i > $i > $i > $o ).
thf(v8_functor0_decl,type,
v8_functor0: $i > $i > $i > $o ).
thf(v12_functor0_decl,type,
v12_functor0: $i > $i > $i > $o ).
thf(v14_functor0_decl,type,
v14_functor0: $i > $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v11_altcat_1_decl,type,
v11_altcat_1: $i > $o ).
thf(v2_yellow18_decl,type,
v2_yellow18: $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(v6_altcat_1_decl,type,
v6_altcat_1: $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(v2_yellow21_decl,type,
v2_yellow21: $i > $o ).
thf(v3_yellow21_decl,type,
v3_yellow21: $i > $o ).
thf(k15_functor0_decl,type,
k15_functor0: $i > $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k6_waybel34_decl,type,
k6_waybel34: $i > $i ).
thf(v21_functor0_decl,type,
v21_functor0: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ( A @ v2_setfam_1 )
=> ( A @ k8_waybel34 @ ( A @ k9_waybel34 @ ( A @ k7_waybel34 @ ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ r3_yellow20 ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( B @ ( C @ v9_functor0 ) ) )
& ( A @ ( B @ ( C @ l2_functor0 ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ l2_functor0 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( B @ ( C @ v11_functor0 ) ) )
& ( A @ ( B @ ( C @ l2_functor0 ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] : ( A @ l1_altcat_1 ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[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(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] : ( A @ l2_altcat_1 ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( A @ v2_setfam_1 ) ) ) ).
thf(61,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v21_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v14_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v12_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v11_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v8_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v6_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel34) ).
thf(365,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v21_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v14_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v12_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v11_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v8_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v6_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(14,axiom,
? [A: $i] : ( A @ l1_altcat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_altcat_1) ).
thf(100,plain,
? [A: $i] : ( A @ l1_altcat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(101,plain,
sk7 @ l1_altcat_1,
inference(cnf,[status(esa)],[100]) ).
thf(22,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(132,plain,
? [A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(133,plain,
( ( sk10 @ v1_altcat_2 )
& ~ ( sk10 @ v3_struct_0 )
& ( sk10 @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
sk10 @ l2_altcat_1,
inference(cnfConj,[status(thm)],[133]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ l1_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_altcat_1) ).
thf(88,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ l1_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(89,plain,
! [A: $i] :
( ( A @ l1_altcat_1 )
| ~ ( A @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[88]) ).
thf(457,plain,
! [A: $i] :
( ( ( sk10 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[134,89]) ).
thf(458,plain,
! [A: $i] :
( ( ( sk10 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[457]) ).
thf(459,plain,
sk10 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( sk10 ))]]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_altcat_1) ).
thf(84,plain,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(85,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnf,[status(esa)],[84]) ).
thf(477,plain,
! [A: $i] :
( ( ( sk10 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[459,85]) ).
thf(478,plain,
! [A: $i] :
( ( ( sk10 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[477]) ).
thf(479,plain,
sk10 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[478:[bind(A,$thf( sk10 ))]]) ).
thf(24,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(139,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)],[24]) ).
thf(140,plain,
( ( sk11 @ v3_yellow21 )
& ( sk11 @ v2_yellow21 )
& ( sk11 @ v1_yellow21 )
& ( sk11 @ v4_yellow18 )
& ( sk11 @ v3_yellow18 )
& ( sk11 @ v2_yellow18 )
& ( sk11 @ v1_altcat_2 )
& ( sk11 @ v12_altcat_1 )
& ( sk11 @ v11_altcat_1 )
& ( sk11 @ v9_altcat_1 )
& ( sk11 @ v6_altcat_1 )
& ( sk11 @ v2_altcat_1 )
& ~ ( sk11 @ v3_struct_0 )
& ( sk11 @ l2_altcat_1 ) ),
inference(cnf,[status(esa)],[139]) ).
thf(149,plain,
sk11 @ l2_altcat_1,
inference(cnfConj,[status(thm)],[140]) ).
thf(56,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_functor0 ) ) )
& ( B @ ( A @ ( C @ v16_functor0 ) ) ) )
=> ( ( B @ ( A @ ( C @ v21_functor0 ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_altcat_2 ) )
& ( A @ ( D @ v3_altcat_2 ) )
& ( D @ v2_altcat_1 )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( B @ ( E @ m1_altcat_2 ) )
& ( B @ ( E @ v3_altcat_2 ) )
& ( E @ v2_altcat_1 )
& ~ ( E @ v3_struct_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ r3_yellow20 ) ) ) ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ ( A @ ( B @ r3_yellow20 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_yellow20) ).
thf(315,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ( B @ v11_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_functor0 ) ) )
& ( B @ ( A @ ( C @ v16_functor0 ) ) ) )
=> ( ( B @ ( A @ ( C @ v21_functor0 ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_altcat_2 ) )
& ( A @ ( D @ v3_altcat_2 ) )
& ( D @ v2_altcat_1 )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( ( B @ ( E @ m1_altcat_2 ) )
& ( B @ ( E @ v3_altcat_2 ) )
& ( E @ v2_altcat_1 )
& ~ ( E @ v3_struct_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ r3_yellow20 ) ) ) ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ ( A @ ( B @ r3_yellow20 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ ( A @ ( B @ r3_yellow20 ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ r3_yellow20 ) ) ) ) )
| ~ ( B @ ( E @ m1_altcat_2 ) )
| ~ ( B @ ( E @ v3_altcat_2 ) )
| ~ ( E @ v2_altcat_1 )
| ( E @ v3_struct_0 )
| ~ ( A @ ( D @ m1_altcat_2 ) )
| ~ ( A @ ( D @ v3_altcat_2 ) )
| ~ ( D @ v2_altcat_1 )
| ( D @ v3_struct_0 )
| ~ ( B @ ( A @ ( C @ v21_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ m2_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ v16_functor0 ) ) )
| ~ ( B @ l2_altcat_1 )
| ~ ( B @ v12_altcat_1 )
| ~ ( B @ v11_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[315]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k8_waybel34 @ ( A @ k9_waybel34 @ ( A @ k7_waybel34 @ ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ r3_yellow20 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_waybel34) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k8_waybel34 @ ( A @ k9_waybel34 @ ( A @ k7_waybel34 @ ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ r3_yellow20 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(70,plain,
~ ! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k8_waybel34 @ ( A @ k9_waybel34 @ ( A @ k7_waybel34 @ ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ r3_yellow20 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(71,plain,
( ~ ( sk1 @ k8_waybel34 @ ( sk1 @ k9_waybel34 @ ( sk1 @ k7_waybel34 @ ( sk1 @ k4_waybel34 @ ( sk1 @ k5_waybel34 @ r3_yellow20 ) ) ) ) )
& ~ ( sk1 @ v2_setfam_1 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
~ ( sk1 @ k8_waybel34 @ ( sk1 @ k9_waybel34 @ ( sk1 @ k7_waybel34 @ ( sk1 @ k4_waybel34 @ ( sk1 @ k5_waybel34 @ r3_yellow20 ) ) ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ ( A @ ( B @ r3_yellow20 ) ) ) ) )
!= ( sk1 @ k8_waybel34 @ ( sk1 @ k9_waybel34 @ ( sk1 @ k7_waybel34 @ ( sk1 @ k4_waybel34 @ ( sk1 @ k5_waybel34 @ r3_yellow20 ) ) ) ) ) )
| ~ $true
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ r3_yellow20 ) ) ) ) )
| ~ ( B @ ( E @ m1_altcat_2 ) )
| ~ ( B @ ( E @ v3_altcat_2 ) )
| ~ ( E @ v2_altcat_1 )
| ( E @ v3_struct_0 )
| ~ ( A @ ( D @ m1_altcat_2 ) )
| ~ ( A @ ( D @ v3_altcat_2 ) )
| ~ ( D @ v2_altcat_1 )
| ( D @ v3_struct_0 )
| ~ ( B @ ( A @ ( C @ v21_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ m2_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ v16_functor0 ) ) )
| ~ ( B @ l2_altcat_1 )
| ~ ( B @ v12_altcat_1 )
| ~ ( B @ v11_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[316,73]) ).
thf(562,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ ( A @ ( B @ r3_yellow20 ) ) ) ) )
!= ( sk1 @ k8_waybel34 @ ( sk1 @ k9_waybel34 @ ( sk1 @ k7_waybel34 @ ( sk1 @ k4_waybel34 @ ( sk1 @ k5_waybel34 @ r3_yellow20 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ r3_yellow20 ) ) ) ) )
| ~ ( B @ ( E @ m1_altcat_2 ) )
| ~ ( B @ ( E @ v3_altcat_2 ) )
| ~ ( E @ v2_altcat_1 )
| ( E @ v3_struct_0 )
| ~ ( A @ ( D @ m1_altcat_2 ) )
| ~ ( A @ ( D @ v3_altcat_2 ) )
| ~ ( D @ v2_altcat_1 )
| ( D @ v3_struct_0 )
| ~ ( B @ ( A @ ( C @ v21_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ m2_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ v16_functor0 ) ) )
| ~ ( B @ l2_altcat_1 )
| ~ ( B @ v12_altcat_1 )
| ~ ( B @ v11_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ( B @ v3_struct_0 )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[561]) ).
thf(581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( sk1 @ k8_waybel34 ) )
| ( E
!= ( sk1 @ k9_waybel34 ) )
| ( ( C @ ( B @ ( A @ k15_functor0 ) ) )
!= ( sk1 @ k7_waybel34 ) )
| ( A
!= ( sk1 @ k4_waybel34 ) )
| ( B
!= ( sk1 @ k5_waybel34 ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ r3_yellow20 ) ) ) ) )
| ~ ( B @ ( E @ m1_altcat_2 ) )
| ~ ( B @ ( E @ v3_altcat_2 ) )
| ~ ( E @ v2_altcat_1 )
| ~ ( A @ ( D @ m1_altcat_2 ) )
| ~ ( A @ ( D @ v3_altcat_2 ) )
| ~ ( D @ v2_altcat_1 )
| ~ ( B @ ( A @ ( C @ v21_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ m2_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ v16_functor0 ) ) )
| ~ ( B @ l2_altcat_1 )
| ~ ( B @ v12_altcat_1 )
| ~ ( B @ v11_altcat_1 )
| ~ ( B @ v2_altcat_1 )
| ~ ( A @ l2_altcat_1 )
| ~ ( A @ v12_altcat_1 )
| ~ ( A @ v11_altcat_1 )
| ~ ( A @ v2_altcat_1 )
| ( E @ v3_struct_0 )
| ( D @ v3_struct_0 )
| ( B @ v3_struct_0 )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[562]) ).
thf(586,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ k15_functor0 ) ) )
!= ( sk1 @ k7_waybel34 ) )
| ~ ( sk1 @ k9_waybel34 @ ( sk1 @ k8_waybel34 @ ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ r3_yellow20 ) ) ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k9_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k8_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v21_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ m2_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v16_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ l2_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ l2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v2_altcat_1 )
| ( sk1 @ k9_waybel34 @ v3_struct_0 )
| ( sk1 @ k8_waybel34 @ v3_struct_0 )
| ( sk1 @ k5_waybel34 @ v3_struct_0 )
| ( sk1 @ k4_waybel34 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[581]) ).
thf(618,plain,
! [A: $i] :
( ( ( sk1 @ k5_waybel34 @ l2_altcat_1 )
!= ( sk11 @ l2_altcat_1 ) )
| ( ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ k15_functor0 ) ) )
!= ( sk1 @ k7_waybel34 ) )
| ~ ( sk1 @ k9_waybel34 @ ( sk1 @ k8_waybel34 @ ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ r3_yellow20 ) ) ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k9_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k8_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v21_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ m2_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v16_functor0 ) ) )
| ~ $true
| ~ ( sk1 @ k5_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ l2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v2_altcat_1 )
| ( sk1 @ k9_waybel34 @ v3_struct_0 )
| ( sk1 @ k8_waybel34 @ v3_struct_0 )
| ( sk1 @ k5_waybel34 @ v3_struct_0 )
| ( sk1 @ k4_waybel34 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[149,586]) ).
thf(619,plain,
! [A: $i] :
( ( ( sk1 @ k5_waybel34 @ l2_altcat_1 )
!= ( sk11 @ l2_altcat_1 ) )
| ( ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ k15_functor0 ) ) )
!= ( sk1 @ k7_waybel34 ) )
| ~ ( sk1 @ k9_waybel34 @ ( sk1 @ k8_waybel34 @ ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ r3_yellow20 ) ) ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k9_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k8_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v21_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ m2_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v16_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ l2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v2_altcat_1 )
| ( sk1 @ k9_waybel34 @ v3_struct_0 )
| ( sk1 @ k8_waybel34 @ v3_struct_0 )
| ( sk1 @ k5_waybel34 @ v3_struct_0 )
| ( sk1 @ k4_waybel34 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[618]) ).
thf(628,plain,
! [A: $i] :
( ( ( sk1 @ k5_waybel34 )
!= sk11 )
| ( ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ k15_functor0 ) ) )
!= ( sk1 @ k7_waybel34 ) )
| ~ ( sk1 @ k9_waybel34 @ ( sk1 @ k8_waybel34 @ ( A @ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ r3_yellow20 ) ) ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k9_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k9_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ m1_altcat_2 ) )
| ~ ( sk1 @ k4_waybel34 @ ( sk1 @ k8_waybel34 @ v3_altcat_2 ) )
| ~ ( sk1 @ k8_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v21_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ m2_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ ( sk1 @ k4_waybel34 @ ( A @ v16_functor0 ) ) )
| ~ ( sk1 @ k5_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k5_waybel34 @ v2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ l2_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v12_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v11_altcat_1 )
| ~ ( sk1 @ k4_waybel34 @ v2_altcat_1 )
| ( sk1 @ k9_waybel34 @ v3_struct_0 )
| ( sk1 @ k8_waybel34 @ v3_struct_0 )
| ( sk1 @ k5_waybel34 @ v3_struct_0 )
| ( sk1 @ k4_waybel34 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[619]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(233,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(234,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[233]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_waybel34 @ ( A @ k8_waybel34 @ m1_altcat_2 ) )
& ( A @ k4_waybel34 @ ( A @ k8_waybel34 @ v3_altcat_2 ) )
& ( A @ k8_waybel34 @ v6_altcat_1 )
& ( A @ k8_waybel34 @ v2_altcat_1 )
& ~ ( A @ k8_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_waybel34) ).
thf(308,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_waybel34 @ ( A @ k8_waybel34 @ m1_altcat_2 ) )
& ( A @ k4_waybel34 @ ( A @ k8_waybel34 @ v3_altcat_2 ) )
& ( A @ k8_waybel34 @ v6_altcat_1 )
& ( A @ k8_waybel34 @ v2_altcat_1 )
& ~ ( A @ k8_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_functor2) ).
thf(202,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(64,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(384,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(142,plain,
sk11 @ v3_yellow18,
inference(cnfConj,[status(thm)],[140]) ).
thf(153,plain,
sk11 @ v11_altcat_1,
inference(cnfConj,[status(thm)],[140]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(237,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(238,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(46,axiom,
? [A: $i] : ( A @ l2_altcat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_altcat_1) ).
thf(266,plain,
? [A: $i] : ( A @ l2_altcat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(267,plain,
sk17 @ l2_altcat_1,
inference(cnf,[status(esa)],[266]) ).
thf(463,plain,
! [A: $i] :
( ( ( sk17 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,89]) ).
thf(464,plain,
! [A: $i] :
( ( ( sk17 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[463]) ).
thf(465,plain,
sk17 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[464:[bind(A,$thf( sk17 ))]]) ).
thf(513,plain,
! [A: $i] :
( ( ( sk17 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,85]) ).
thf(514,plain,
! [A: $i] :
( ( ( sk17 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[513]) ).
thf(515,plain,
sk17 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( sk17 ))]]) ).
thf(723,plain,
! [A: $i] :
( ( A != sk17 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,515]) ).
thf(724,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk17 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( sk17 ))]]) ).
thf(41,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(240,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)],[41]) ).
thf(241,plain,
! [A: $i] :
( ( ( A @ sk13 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk13 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk13 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(244,plain,
! [A: $i] :
( ( A @ sk13 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(433,plain,
! [A: $i] :
( ( ( sk7 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,85]) ).
thf(434,plain,
! [A: $i] :
( ( ( sk7 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[433]) ).
thf(435,plain,
sk7 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( sk7 ))]]) ).
thf(717,plain,
! [A: $i] :
( ( A != sk7 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,435]) ).
thf(718,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk7 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( sk7 ))]]) ).
thf(1311,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk7 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true
| ( A @ sk13 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[244,718]) ).
thf(1312,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk7 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk13 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1313,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk7 @ sk13 @ v1_finset_1 ) ),
inference(pattern_uni,[status(thm)],[1312:[bind(A,$thf( sk7 ))]]) ).
thf(26,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(157,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)],[26]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( B @ v1_altcat_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_functor0) ).
thf(284,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( B @ v1_altcat_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(eqfactor_ordered,[status(thm)],[75]) ).
thf(415,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[414:[bind(A,$thf( B ))]]) ).
thf(416,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[415]) ).
thf(152,plain,
sk11 @ v2_yellow18,
inference(cnfConj,[status(thm)],[140]) ).
thf(51,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(289,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)],[51]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l1_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_functor0) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l1_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,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(216,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)],[36]) ).
thf(147,plain,
sk11 @ v2_altcat_1,
inference(cnfConj,[status(thm)],[140]) ).
thf(733,plain,
! [A: $i] :
( ( A != sk10 )
| ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,459]) ).
thf(734,plain,
( ( k1_xboole_0 @ l1_altcat_1 )
| ~ ( sk10 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[733:[bind(A,$thf( sk10 ))]]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v21_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v16_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v14_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v12_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v11_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v9_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v8_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v6_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_waybel34) ).
thf(396,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v21_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v16_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v14_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v12_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v11_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v9_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v8_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v6_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(45,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(262,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(263,plain,
( ( sk16 @ v1_finset_1 )
& ~ ( sk16 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[262]) ).
thf(265,plain,
sk16 @ v1_finset_1,
inference(cnfConj,[status(thm)],[263]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(117,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(102,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(103,plain,
! [A: $i] : ( A @ ( A @ sk8 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[102]) ).
thf(217,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[216]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ v1_xboole_0 )
| ~ ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[217]) ).
thf(436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( D @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
| ~ ( D @ v1_xboole_0 )
| ~ $true
| ~ ( C @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[103,218]) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ m1_subset_1 ) )
!= ( D @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
| ~ ( D @ v1_xboole_0 )
| ~ ( C @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[436]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( B @ k1_zfmisc_1 @ sk8 @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( F @ k1_zfmisc_1 )),bind(B,$thf( B )),bind(C,$thf( F @ k1_zfmisc_1 @ sk8 )),bind(D,$thf( F ))]]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( B @ k1_zfmisc_1 @ sk8 @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[438]) ).
thf(48,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(270,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ? [B: $i] : ( A @ ( B @ m1_altcat_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(53,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(300,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(301,plain,
~ ? [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[300]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[301]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_functor0) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(252,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(57,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(317,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)],[57]) ).
thf(141,plain,
~ ( sk11 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[140]) ).
thf(44,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(256,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)],[44]) ).
thf(4,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(76,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)],[4]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B @ v1_finset_1 )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[76]) ).
thf(135,plain,
~ ( sk10 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[133]) ).
thf(1038,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,135]) ).
thf(1039,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk10 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( sk10 ))]]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_functor2) ).
thf(212,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,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(96,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)],[12]) ).
thf(72,plain,
~ ( sk1 @ v2_setfam_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(1048,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,72]) ).
thf(1049,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( sk1 ))]]) ).
thf(1244,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true
| ( A @ sk13 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[244,1049]) ).
thf(1245,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( A @ sk13 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1246,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( sk1 @ sk13 @ v1_finset_1 ) ),
inference(pattern_uni,[status(thm)],[1245:[bind(A,$thf( sk1 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( ( A @ sk12 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ sk12 @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k1_zfmisc_1 @ ( A @ sk12 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[157]) ).
thf(161,plain,
! [A: $i] :
( ( A @ sk12 @ v1_finset_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[158]) ).
thf(1247,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true
| ( A @ sk12 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[161,1049]) ).
thf(1248,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( A @ sk12 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[1247]) ).
thf(1249,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ( sk1 @ sk12 @ v1_finset_1 ) ),
inference(pattern_uni,[status(thm)],[1248:[bind(A,$thf( sk1 ))]]) ).
thf(52,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(298,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)],[52]) ).
thf(69,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k9_waybel34 @ ( A @ k8_waybel34 @ ( A @ k6_waybel34 @ ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ r3_yellow20 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_waybel34) ).
thf(412,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k9_waybel34 @ ( A @ k8_waybel34 @ ( A @ k6_waybel34 @ ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ r3_yellow20 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(148,plain,
sk11 @ v1_yellow21,
inference(cnfConj,[status(thm)],[140]) ).
thf(264,plain,
~ ( sk16 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[263]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(375,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(150,plain,
sk11 @ v3_yellow21,
inference(cnfConj,[status(thm)],[140]) ).
thf(731,plain,
! [A: $i] :
( ( A != sk11 )
| ( k1_xboole_0 @ v3_yellow21 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,150]) ).
thf(732,plain,
( ( k1_xboole_0 @ v3_yellow21 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( sk11 ))]]) ).
thf(118,plain,
! [A: $i] :
( ( A @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[117]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ m2_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v16_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v9_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_waybel34) ).
thf(391,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ m2_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v16_functor0 ) ) )
& ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ ( A @ k7_waybel34 @ v9_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(144,plain,
sk11 @ v2_yellow21,
inference(cnfConj,[status(thm)],[140]) ).
thf(59,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(335,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)],[59]) ).
thf(60,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ v3_yellow21 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v1_yellow21 )
& ( A @ k4_waybel34 @ v4_yellow18 )
& ( A @ k4_waybel34 @ v3_yellow18 )
& ( A @ k4_waybel34 @ v2_yellow18 )
& ( A @ k4_waybel34 @ v1_altcat_2 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v9_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel34) ).
thf(350,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ v3_yellow21 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v1_yellow21 )
& ( A @ k4_waybel34 @ v4_yellow18 )
& ( A @ k4_waybel34 @ v3_yellow18 )
& ( A @ k4_waybel34 @ v2_yellow18 )
& ( A @ k4_waybel34 @ v1_altcat_2 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v9_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l2_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_functor0) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l2_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( ( A @ k7_waybel34 @ ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ k15_functor0 ) ) )
= ( A @ k6_waybel34 ) )
& ( ( A @ k6_waybel34 @ ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ k15_functor0 ) ) )
= ( A @ k7_waybel34 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_waybel34) ).
thf(406,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( ( A @ k7_waybel34 @ ( A @ k4_waybel34 @ ( A @ k5_waybel34 @ k15_functor0 ) ) )
= ( A @ k6_waybel34 ) )
& ( ( A @ k6_waybel34 @ ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ k15_functor0 ) ) )
= ( A @ k7_waybel34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(18,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(113,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,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(219,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)],[37]) ).
thf(63,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(377,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)],[63]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_functor0) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(253,plain,
( ~ ( sk15 @ v3_struct_0 )
& ( sk15 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[252]) ).
thf(255,plain,
~ ( sk15 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[253]) ).
thf(1042,plain,
! [A: $i] :
( ( A != sk15 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,255]) ).
thf(1043,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk15 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1042:[bind(A,$thf( sk15 ))]]) ).
thf(34,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(208,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)],[34]) ).
thf(449,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ $true
| ( A @ sk12 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[161,264]) ).
thf(450,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ( A @ sk12 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[449]) ).
thf(451,plain,
sk16 @ sk12 @ v1_finset_1,
inference(pattern_uni,[status(thm)],[450:[bind(A,$thf( sk16 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ( A @ l1_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l1_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_functor0) ).
thf(98,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ( A @ l1_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l1_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ m2_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_waybel34) ).
thf(303,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ m2_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(65,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(387,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)],[65]) ).
thf(725,plain,
! [A: $i] :
( ( A != sk11 )
| ( k1_xboole_0 @ v2_yellow21 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,144]) ).
thf(726,plain,
( ( k1_xboole_0 @ v2_yellow21 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( sk11 ))]]) ).
thf(10,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(90,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(91,plain,
sk4 @ l1_struct_0,
inference(cnf,[status(esa)],[90]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l1_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v11_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_functor0) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l1_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v11_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_functor0) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(460,plain,
! [A: $i] :
( ( ( sk11 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,89]) ).
thf(461,plain,
! [A: $i] :
( ( ( sk11 @ l2_altcat_1 )
!= ( A @ l2_altcat_1 ) )
| ( A @ l1_altcat_1 ) ),
inference(simp,[status(thm)],[460]) ).
thf(462,plain,
sk11 @ l1_altcat_1,
inference(pattern_uni,[status(thm)],[461:[bind(A,$thf( sk11 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_functor0) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,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(162,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)],[27]) ).
thf(21,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(123,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)],[21]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ l2_functor0 ) ) )
& ( B @ l1_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ l2_functor0 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ v9_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_functor0) ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ l2_functor0 ) ) )
& ( B @ l1_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ l2_functor0 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k15_functor0 ) ) @ v9_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(145,plain,
sk11 @ v9_altcat_1,
inference(cnfConj,[status(thm)],[140]) ).
thf(1228,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ~ $true
| ( A @ sk13 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[244,264]) ).
thf(1229,plain,
! [A: $i] :
( ( ( A @ v1_xboole_0 )
!= ( sk16 @ v1_xboole_0 ) )
| ( A @ sk13 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[1228]) ).
thf(1230,plain,
sk16 @ sk13 @ v1_finset_1,
inference(pattern_uni,[status(thm)],[1229:[bind(A,$thf( sk16 ))]]) ).
thf(154,plain,
sk11 @ v12_altcat_1,
inference(cnfConj,[status(thm)],[140]) ).
thf(385,plain,
~ ! [A: $i] : ( A @ v2_setfam_1 ),
inference(miniscope,[status(thm)],[384]) ).
thf(386,plain,
~ ( sk21 @ v2_setfam_1 ),
inference(cnf,[status(esa)],[385]) ).
thf(143,plain,
sk11 @ v4_yellow18,
inference(cnfConj,[status(thm)],[140]) ).
thf(495,plain,
! [A: $i] :
( ( ( sk11 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[462,85]) ).
thf(496,plain,
! [A: $i] :
( ( ( sk11 @ l1_altcat_1 )
!= ( A @ l1_altcat_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[495]) ).
thf(497,plain,
sk11 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( sk11 ))]]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk3 ) @ l2_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnf,[status(esa)],[86]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_functor2) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,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(186,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)],[29]) ).
thf(28,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(171,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)],[28]) ).
thf(20,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(119,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)],[20]) ).
thf(39,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(235,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)],[39]) ).
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 ) )
=> ( ( 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(272,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)],[49]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk2 ) @ v9_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) )
& ( ( B @ ( A @ ( A @ ( B @ sk2 ) @ l2_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk2 ) @ l2_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(151,plain,
sk11 @ v1_altcat_2,
inference(cnfConj,[status(thm)],[140]) ).
thf(146,plain,
sk11 @ v6_altcat_1,
inference(cnfConj,[status(thm)],[140]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_waybel34 @ l2_altcat_1 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_waybel34) ).
thf(326,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_waybel34 @ l2_altcat_1 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(136,plain,
sk10 @ v1_altcat_2,
inference(cnfConj,[status(thm)],[133]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_functor0) ).
thf(268,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ l1_functor0 ) ) )
| ~ ( B @ ( A @ ( C @ l2_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnf,[status(esa)],[78]) ).
thf(719,plain,
! [A: $i] :
( ( A != sk11 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[239,141]) ).
thf(720,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk11 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( sk11 ))]]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk5 ) @ v11_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) )
& ( ( B @ ( A @ ( A @ ( B @ sk5 ) @ l2_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk5 ) @ l2_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_functor0) ).
thf(200,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(254,plain,
sk15 @ l1_struct_0,
inference(cnfConj,[status(thm)],[253]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk2 ) @ v9_functor0 ) ) )
| ~ ( B @ l1_altcat_1 )
| ~ ( A @ l1_altcat_1 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(17,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(111,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)],[17]) ).
thf(23336,plain,
$false,
inference(e,[status(thm)],[365,101,479,628,234,88,308,202,384,142,153,724,1313,157,284,416,152,289,316,78,216,84,147,734,132,396,89,265,74,233,117,439,270,85,102,302,70,137,92,252,435,317,141,256,77,1039,212,96,1246,515,1249,134,73,237,244,266,586,718,298,412,148,264,161,149,375,732,118,391,144,335,350,86,406,113,219,377,245,1043,208,451,76,98,303,387,103,726,91,240,155,198,462,135,267,80,162,255,123,1049,194,145,150,1230,154,72,386,143,497,465,87,218,104,186,171,139,75,119,235,272,82,151,300,315,262,146,326,239,136,268,79,720,94,459,200,254,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT376+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
% 0.16/0.42 % Computer : n001.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 21:38:56 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/1.31 % [INFO] Parsing done (285ms).
% 1.77/1.32 % [INFO] Running in sequential loop mode.
% 2.66/1.73 % [INFO] eprover registered as external prover.
% 2.66/1.74 % [INFO] Scanning for conjecture ...
% 2.82/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 126 axioms. Running axiom selection ...
% 2.99/1.99 % [INFO] Axiom selection finished. Selected 67 axioms (removed 59 axioms).
% 3.44/2.12 % [INFO] Problem is first-order (TPTP FOF).
% 3.80/2.13 % [INFO] Type checking passed.
% 3.80/2.14 % [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 ...
% 82.86/19.44 % External prover 'e' found a proof!
% 82.86/19.44 % [INFO] Killing All external provers ...
% 82.86/19.45 % Time passed: 18877ms (effective reasoning time: 18119ms)
% 82.86/19.45 % 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)>
% 82.86/19.45 % Axioms used in derivation (67): dt_l2_altcat_1, t5_subset, rc9_functor0, cc2_setfam_1, rc3_finset_1, rc2_setfam_1, existence_m1_altcat_2, rc7_functor0, cc2_finset_1, cc4_functor0, dt_k7_waybel34, dt_l1_altcat_1, t52_yellow20, rc4_finset_1, dt_k9_waybel34, cc2_yellow21, t1_subset, fc5_waybel34, existence_m2_functor0, rc8_functor0, cc5_yellow21, dt_k15_functor0, t6_boole, fc6_waybel34, cc8_yellow21, rc3_setfam_1, cc7_yellow21, existence_l2_functor0, existence_l2_altcat_1, cc2_functor0, t4_subset, t7_boole, cc1_funct_1, dt_m1_altcat_2, rc3_struct_0, t56_waybel34, t18_waybel34, cc1_functor2, cc1_yellow21, existence_m1_subset_1, cc6_functor0, existence_l1_altcat_1, rc3_functor0, dt_k4_waybel34, fc1_struct_0, rc1_yellow21, dt_k5_waybel34, cc11_yellow21, cc9_yellow21, dt_k6_waybel34, rc1_finset_1, dt_k8_waybel34, cc4_functor2, cc1_finset_1, fc8_waybel34, t8_boole, dt_m2_functor0, rc5_functor0, rc5_struct_0, t2_subset, cc5_functor2, existence_l1_struct_0, fc7_waybel34, cc6_yellow21, dt_l2_functor0, antisymmetry_r2_hidden, existence_l1_functor0
% 82.86/19.45 % No. of inferences in proof: 264
% 82.86/19.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18877 ms resp. 18119 ms w/o parsing
% 83.20/19.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.20/19.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------