%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX063+1 : TPTP v9.3.1. Released v9.1.0.
% 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 : n013.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 09:15:04 AM UTC 2026
% Result : Theorem 66.90s 15.79s
% Output : Refutation 69.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 386
% Syntax : Number of formulae : 848 ( 125 unt; 0 typ; 45 def)
% Number of atoms : 3248 ( 996 equ; 0 cnn)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 9007 ( 671 ~; 722 |; 903 &;5981 @)
% ( 64 <=>; 666 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 121 usr; 5 con; 0-3 aty)
% Number of variables : 2502 ( 84 ^;2165 !; 208 ?;2502 :)
% ( 0 !>; 0 ?*; 0 @-; 45 @+)
% Comments :
%------------------------------------------------------------------------------
thf(list_succeeds_decl,type,
list_succeeds: $i > $o ).
thf(rev_decl,type,
rev: $i > $i ).
thf(plus_succeeds_decl,type,
plus_succeeds: $i > $i > $i > $o ).
thf(plus_terminates_decl,type,
plus_terminates: $i > $i > $i > $o ).
thf(nat_succeeds_decl,type,
nat_succeeds: $i > $o ).
thf(plus_fails_decl,type,
plus_fails: $i > $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf('0_decl',type,
'0': $i ).
thf('@*_decl',type,
'@*': $i > $i > $i ).
thf('@=<_terminates_decl',type,
'@=<_terminates': $i > $i > $o ).
thf('@=<_succeeds_decl',type,
'@=<_succeeds': $i > $i > $o ).
thf('@=<_fails_decl',type,
'@=<_fails': $i > $i > $o ).
thf(nat_terminates_decl,type,
nat_terminates: $i > $o ).
thf(nat_fails_decl,type,
nat_fails: $i > $o ).
thf(member2_terminates_decl,type,
member2_terminates: $i > $i > $i > $o ).
thf(member2_succeeds_decl,type,
member2_succeeds: $i > $i > $i > $o ).
thf(member2_fails_decl,type,
member2_fails: $i > $i > $i > $o ).
thf(gr_decl,type,
gr: $i > $o ).
thf(not_same_occ_fails_decl,type,
not_same_occ_fails: $i > $i > $o ).
thf(occ_fails_decl,type,
occ_fails: $i > $i > $i > $o ).
thf('@<_terminates_decl',type,
'@<_terminates': $i > $i > $o ).
thf('@<_succeeds_decl',type,
'@<_succeeds': $i > $i > $o ).
thf('@<_fails_decl',type,
'@<_fails': $i > $i > $o ).
thf(times_terminates_decl,type,
times_terminates: $i > $i > $i > $o ).
thf(times_fails_decl,type,
times_fails: $i > $i > $i > $o ).
thf(nat_list_terminates_decl,type,
nat_list_terminates: $i > $o ).
thf(nat_list_succeeds_decl,type,
nat_list_succeeds: $i > $o ).
thf(nat_list_fails_decl,type,
nat_list_fails: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(sub_decl,type,
sub: $i > $i > $o ).
thf(member_succeeds_decl,type,
member_succeeds: $i > $i > $o ).
thf('@+_decl',type,
'@+': $i > $i > $i ).
thf(permutation_fails_decl,type,
permutation_fails: $i > $i > $o ).
thf(delete_fails_decl,type,
delete_fails: $i > $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(reverse_succeeds_decl,type,
reverse_succeeds: $i > $i > $o ).
thf(a_reverse_succeeds_decl,type,
a_reverse_succeeds: $i > $i > $i > $o ).
thf(delete_succeeds_decl,type,
delete_succeeds: $i > $i > $i > $o ).
thf(a_reverse_terminates_decl,type,
a_reverse_terminates: $i > $i > $i > $o ).
thf(a_reverse_fails_decl,type,
a_reverse_fails: $i > $i > $i > $o ).
thf(permutation_succeeds_decl,type,
permutation_succeeds: $i > $i > $o ).
thf(occ_decl,type,
occ: $i > $i > $i ).
thf(member_terminates_decl,type,
member_terminates: $i > $i > $o ).
thf(list_terminates_decl,type,
list_terminates: $i > $o ).
thf('**_decl',type,
'**': $i > $i > $i ).
thf(reverse_terminates_decl,type,
reverse_terminates: $i > $i > $o ).
thf(permutation_terminates_decl,type,
permutation_terminates: $i > $i > $o ).
thf(length_succeeds_decl,type,
length_succeeds: $i > $i > $o ).
thf(reverse_fails_decl,type,
reverse_fails: $i > $i > $o ).
thf(n_reverse_succeeds_decl,type,
n_reverse_succeeds: $i > $i > $o ).
thf(n_reverse_terminates_decl,type,
n_reverse_terminates: $i > $i > $o ).
thf(n_reverse_fails_decl,type,
n_reverse_fails: $i > $i > $o ).
thf(append_terminates_decl,type,
append_terminates: $i > $i > $i > $o ).
thf(list_fails_decl,type,
list_fails: $i > $o ).
thf(lh_decl,type,
lh: $i > $i ).
thf(append_fails_decl,type,
append_fails: $i > $i > $i > $o ).
thf(append_succeeds_decl,type,
append_succeeds: $i > $i > $i > $o ).
thf(delete_terminates_decl,type,
delete_terminates: $i > $i > $i > $o ).
thf(member_fails_decl,type,
member_fails: $i > $i > $o ).
thf(same_occ_terminates_decl,type,
same_occ_terminates: $i > $i > $o ).
thf(same_occ_succeeds_decl,type,
same_occ_succeeds: $i > $i > $o ).
thf(same_occ_fails_decl,type,
same_occ_fails: $i > $i > $o ).
thf(length_terminates_decl,type,
length_terminates: $i > $i > $o ).
thf(occ_succeeds_decl,type,
occ_succeeds: $i > $i > $i > $o ).
thf(occ_terminates_decl,type,
occ_terminates: $i > $i > $i > $o ).
thf(not_same_occ_terminates_decl,type,
not_same_occ_terminates: $i > $i > $o ).
thf(length_fails_decl,type,
length_fails: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk19_decl,type,
sk19: $i > $i > $o ).
thf(sk20_decl,type,
sk20: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i ).
thf(sk37_decl,type,
sk37: $i > $i > $o ).
thf(sk38_decl,type,
sk38: $i > $i > $i ).
thf(sk39_decl,type,
sk39: $i > $i > $i ).
thf(sk40_decl,type,
sk40: $i > $i > $i ).
thf(sk49_decl,type,
sk49: $i > $i ).
thf(sk50_decl,type,
sk50: $i > $i ).
thf(sk51_decl,type,
sk51: $i > $i > $o ).
thf(sk52_decl,type,
sk52: $i > $i > $i ).
thf(sk53_decl,type,
sk53: $i > $i > $i ).
thf(sk54_decl,type,
sk54: $i > $i > $i ).
thf(sk55_decl,type,
sk55: $i > $i > $i ).
thf(sk56_decl,type,
sk56: $i > $i > $i ).
thf(sk57_decl,type,
sk57: $i > $i > $i ).
thf(sk81_decl,type,
sk81: $i > $i ).
thf(sk90_decl,type,
sk90: $i > $i > $i > $o ).
thf(sk91_decl,type,
sk91: $i > $i > $i > $i ).
thf(sk92_decl,type,
sk92: $i > $i > $i > $i ).
thf(sk93_decl,type,
sk93: $i > $i > $o ).
thf(sk94_decl,type,
sk94: $i > $i > $i > $i ).
thf(sk95_decl,type,
sk95: $i > $i > $i > $i ).
thf(sk96_decl,type,
sk96: $i > $i > $i ).
thf(sk97_decl,type,
sk97: $i > $i > $i ).
thf(sk104_decl,type,
sk104: $i > $i > $o ).
thf(sk105_decl,type,
sk105: $i > $i > $i > $i ).
thf(sk106_decl,type,
sk106: $i > $i > $i > $i ).
thf(sk107_decl,type,
sk107: $i > $i > $o ).
thf(sk108_decl,type,
sk108: $i > $i > $i ).
thf(sk109_decl,type,
sk109: $i > $i > $i ).
thf(sk110_decl,type,
sk110: $i > $i > $i ).
thf(sk118_decl,type,
sk118: $i > $i ).
thf(sk119_decl,type,
sk119: $i > $i ).
thf(sk121_decl,type,
sk121: $i > $i > $i ).
thf(sk122_decl,type,
sk122: $i > $i > $i ).
thf(sk123_decl,type,
sk123: $i > $i > $i ).
thf(sk124_decl,type,
sk124: $i > $i > $o ).
thf(sk125_decl,type,
sk125: $i > $i > $i ).
thf(sk126_decl,type,
sk126: $i > $i > $i ).
thf(sk127_decl,type,
sk127: $i > $i > $i ).
thf(sk128_decl,type,
sk128: $i > $i > $o ).
thf(sk129_decl,type,
sk129: $i > $i > $i ).
thf(sk130_decl,type,
sk130: $i > $i > $i ).
thf(sk131_decl,type,
sk131: $i > $i > $i ).
thf(sk139_decl,type,
sk139: $i > $i > $i ).
thf(sk140_decl,type,
sk140: $i > $i > $i ).
thf(sk150_decl,type,
sk150: $i > $i ).
thf(sk165_decl,type,
sk165: $i > $i ).
thf(sk166_decl,type,
sk166: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ list_succeeds )
=> ( ( A @ rev @ rev )
= A ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ! [E: $i] :
( ( D @ ( E @ permutation_fails ) )
| ( E @ ( B @ ( C @ delete_fails ) ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ! [D: $i] :
( ( C @ ( D @ permutation_fails ) )
| ( D @ ( B @ ( B @ ( A @ sk20 ) @ delete_fails ) ) ) )
| ( A
!= ( C @ ( B @ ( A @ sk20 ) @ cons ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( A @ sk21 ) @ ( C @ permutation_fails ) )
| ( C @ ( B @ ( B @ ( A @ sk20 ) @ delete_fails ) ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i] :
@+[B: $i] :
~ ! [C: $i] :
( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ nat_list_fails )
| ( A @ sk26 @ nat_fails )
| ( A
!= ( B @ ( A @ sk26 @ cons ) ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
? [D: $i] :
( ? [E: $i] :
( ( E @ ( D @ length_succeeds ) )
& ( A
= ( E @ s ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( C @ length_succeeds ) )
& ( A
= ( D @ s ) ) )
& ( B
= ( C @ ( B @ ( A @ sk38 ) @ cons ) ) ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( B @ ( A @ sk39 ) @ length_succeeds ) )
& ( A
= ( C @ s ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: $i] :
@+[B: $i] :
~ ! [C: $i] :
( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ list_fails )
| ( A
!= ( B @ ( A @ sk49 @ cons ) ) ) ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( C @ '@<_succeeds' ) )
& ( A
= ( D @ s ) ) )
& ( B
= ( C @ s ) ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( B @ ( A @ sk52 ) @ '@<_succeeds' ) )
& ( A
= ( C @ s ) ) ) ) ) ).
thf(sk54_def,definition,
( sk54
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( A
= ( C @ s ) ) ) ) ).
thf(sk55_def,definition,
( sk55
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ! [E: $i] :
( ( A @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ! [D: $i] :
( ( A @ ( nil @ ( B @ ( A @ sk55 ) @ cons ) @ ( D @ append_fails ) ) )
| ( D @ ( C @ n_reverse_fails ) ) )
| ( B
!= ( C @ ( B @ ( A @ sk55 ) @ cons ) ) ) ) ) ) ).
thf(sk57_def,definition,
( sk57
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( nil @ ( B @ ( A @ sk55 ) @ cons ) @ ( C @ append_fails ) ) )
| ( C @ ( B @ ( A @ sk56 ) @ n_reverse_fails ) ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ nat_fails )
| ( A
!= ( B @ s ) ) ) ) ) ).
thf(sk91_def,definition,
( sk91
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( A @ ( E @ ( C @ occ_fails ) ) )
| ( C = D )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ) ).
thf(sk92_def,definition,
( sk92
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ ( C @ occ_fails ) ) )
| ( C
= ( C @ ( B @ ( A @ sk91 ) ) ) )
| ( B
!= ( D @ ( C @ ( B @ ( A @ sk91 ) ) @ cons ) ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ! [E: $i] :
( ( E @ ( D @ ( C @ occ_fails ) ) )
| ( A
!= ( E @ s ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk95_def,definition,
( sk95
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ ( C @ ( B @ ( A @ sk94 ) ) @ ( C @ occ_fails ) ) )
| ( A
!= ( D @ s ) ) ) ) ) ).
thf(sk96_def,definition,
( sk96
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( C @ '@=<_succeeds' ) )
& ( A
= ( D @ s ) ) )
& ( B
= ( C @ s ) ) ) ) ) ).
thf(sk97_def,definition,
( sk97
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( B @ ( A @ sk96 ) @ '@=<_succeeds' ) )
& ( A
= ( C @ s ) ) ) ) ) ).
thf(sk105_def,definition,
( sk105
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ! [E: $i] :
( ( A @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) ) )
| ( C
!= ( D @ s ) ) ) ) ) ).
thf(sk106_def,definition,
( sk106
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ ( B @ plus_fails ) ) )
| ( D @ ( B @ ( C @ ( B @ ( A @ sk105 ) ) @ times_fails ) ) ) ) ) ) ).
thf(sk108_def,definition,
( sk108
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ permutation_succeeds ) )
& ( E @ ( B @ ( C @ delete_succeeds ) ) ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk109_def,definition,
( sk109
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ permutation_succeeds ) )
& ( D @ ( B @ ( B @ ( A @ sk108 ) @ delete_succeeds ) ) ) )
& ( A
= ( C @ ( B @ ( A @ sk108 ) @ cons ) ) ) ) ) ) ).
thf(sk110_def,definition,
( sk110
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk109 ) @ ( C @ permutation_succeeds ) )
& ( C @ ( B @ ( B @ ( A @ sk108 ) @ delete_succeeds ) ) ) ) ) ) ).
thf(sk118_def,definition,
( sk118
= ( ^ [A: $i] :
@+[B: $i] :
? [C: $i] :
( ( C @ nat_list_succeeds )
& ( B @ nat_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ) ).
thf(sk119_def,definition,
( sk119
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ nat_list_succeeds )
& ( A @ sk118 @ nat_succeeds )
& ( A
= ( B @ ( A @ sk118 @ cons ) ) ) ) ) ) ).
thf(sk121_def,definition,
( sk121
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
? [D: $i] :
( ? [E: $i] :
( ( A @ ( nil @ ( C @ cons ) @ ( E @ append_succeeds ) ) )
& ( E @ ( D @ n_reverse_succeeds ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk122_def,definition,
( sk122
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( A @ ( nil @ ( B @ ( A @ sk121 ) @ cons ) @ ( D @ append_succeeds ) ) )
& ( D @ ( C @ n_reverse_succeeds ) ) )
& ( B
= ( C @ ( B @ ( A @ sk121 ) @ cons ) ) ) ) ) ) ).
thf(sk123_def,definition,
( sk123
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( nil @ ( B @ ( A @ sk121 ) @ cons ) @ ( C @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ sk122 ) @ n_reverse_succeeds ) ) ) ) ) ).
thf(sk125_def,definition,
( sk125
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ! [E: $i] :
( ( E @ ( D @ length_fails ) )
| ( A
!= ( E @ s ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ) ).
thf(sk126_def,definition,
( sk126
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ! [D: $i] :
( ( D @ ( C @ length_fails ) )
| ( A
!= ( D @ s ) ) )
| ( B
!= ( C @ ( B @ ( A @ sk125 ) @ cons ) ) ) ) ) ) ).
thf(sk127_def,definition,
( sk127
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ ( B @ ( A @ sk126 ) @ length_fails ) )
| ( A
!= ( C @ s ) ) ) ) ) ).
thf(sk129_def,definition,
( sk129
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ! [D: $i] :
( ( D @ ( C @ '@<_fails' ) )
| ( A
!= ( D @ s ) ) )
| ( B
!= ( C @ s ) ) ) ) ) ).
thf(sk130_def,definition,
( sk130
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ ( B @ ( A @ sk129 ) @ '@<_fails' ) )
| ( A
!= ( C @ s ) ) ) ) ) ).
thf(sk131_def,definition,
( sk131
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( A
= ( C @ s ) ) ) ) ).
thf(sk139_def,definition,
( sk139
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ! [D: $i] :
( ( D @ ( C @ '@=<_fails' ) )
| ( A
!= ( D @ s ) ) )
| ( B
!= ( C @ s ) ) ) ) ) ).
thf(sk140_def,definition,
( sk140
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ ( B @ ( A @ sk139 ) @ '@=<_fails' ) )
| ( A
!= ( C @ s ) ) ) ) ) ).
thf(sk150_def,definition,
( sk150
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ nat_succeeds )
& ( A
= ( B @ s ) ) ) ) ) ).
thf(sk165_def,definition,
( sk165
= ( ^ [A: $i] :
@+[B: $i] :
? [C: $i] :
( ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ) ).
thf(sk166_def,definition,
( sk166
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ list_succeeds )
& ( A
= ( B @ ( A @ sk165 @ cons ) ) ) ) ) ) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
<=> ( ? [C: $i] :
( ( B
= ( C @ s ) )
& ( A = '0' ) )
| ? [C: $i,D: $i] :
( ( D @ ( C @ '@<_succeeds' ) )
& ( B
= ( D @ s ) )
& ( A
= ( C @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id103) ).
thf(809,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( B
= ( C @ s ) )
& ( A = '0' ) )
| ? [C: $i,D: $i] :
( ( D @ ( C @ '@<_succeeds' ) )
& ( B
= ( D @ s ) )
& ( A
= ( C @ s ) ) ) )
=> ( B @ ( A @ '@<_succeeds' ) ) )
& ( ( B @ ( A @ '@<_succeeds' ) )
=> ( ? [C: $i] :
( ( B
= ( C @ s ) )
& ( A = '0' ) )
| ? [C: $i,D: $i] :
( ( D @ ( C @ '@<_succeeds' ) )
& ( B
= ( D @ s ) )
& ( A
= ( C @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ delete_succeeds ) ) )
& ( B @ list_succeeds ) )
=> ( ( B @ ( A @ occ ) )
= ( C @ ( A @ occ ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:occ:eq)') ).
thf(1879,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ delete_succeeds ) ) )
& ( B @ list_succeeds ) )
=> ( ( B @ ( A @ occ ) )
= ( C @ ( A @ occ ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( '0' @ s @ ( A @ '@*' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:one)_005') ).
thf(1411,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( '0' @ s @ ( A @ '@*' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_succeeds ) ) )
=> ( C @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:ground)') ).
thf(1168,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_succeeds ) ) )
=> ( C @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ? [C: $i] : ( C @ ( B @ ( A @ append_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:existence)') ).
thf(1767,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ? [C: $i] : ( C @ ( B @ ( A @ append_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( D @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:uniqueness:1)') ).
thf(1995,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( D @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ list_succeeds )
=> ( ( A @ rev @ rev )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(rev:involution)') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ list_succeeds )
=> ( ( A @ rev @ rev )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(343,plain,
~ ! [A: $i] :
( ( A @ list_succeeds )
=> ( ( A @ rev @ rev )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(344,plain,
( ( ( sk1 @ rev @ rev )
!= sk1 )
& ( sk1 @ list_succeeds ) ),
inference(cnf,[status(esa)],[343]) ).
thf(346,plain,
( ( sk1 @ rev @ rev )
!= sk1 ),
inference(cnfConj,[status(thm)],[344]) ).
thf(347,plain,
( ( sk1 @ rev @ rev )
!= sk1 ),
inference(lifteq,[status(thm)],[346]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ member_fails ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member:termination)_014') ).
thf(1729,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ member_fails ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(329,axiom,
! [A: $i] :
( ( A @ list_succeeds )
<=> ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id88) ).
thf(1970,plain,
! [A: $i] :
( ( ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ list_succeeds ) )
& ( ( A @ list_succeeds )
=> ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1971,plain,
( ! [A: $i] :
( ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ list_succeeds ) )
& ! [A: $i] :
( ( A @ list_succeeds )
=> ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1970]) ).
thf(1972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ list_succeeds )
| ( B != nil ) )
& ( ( B @ list_succeeds )
| ~ ( D @ list_succeeds )
| ( B
!= ( D @ ( C @ cons ) ) ) )
& ( ( A = nil )
| ( A @ sk166 @ list_succeeds )
| ~ ( A @ list_succeeds ) )
& ( ( A = nil )
| ( A
= ( A @ sk166 @ ( A @ sk165 @ cons ) ) )
| ~ ( A @ list_succeeds ) ) ),
inference(cnf,[status(esa)],[1971]) ).
thf(1976,plain,
! [A: $i] :
( ( A @ list_succeeds )
| ( A != nil ) ),
inference(cnfConj,[status(thm)],[1972]) ).
thf(1981,plain,
! [A: $i] :
( ( A @ list_succeeds )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[1976]) ).
thf(1982,plain,
nil @ list_succeeds,
inference(simp,[status(thm)],[1981]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ gr )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( B @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:ground:3)') ).
thf(468,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ gr )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( B @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ list_succeeds )
=> ( C @ ( B @ ( A @ append_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:termination:2)') ).
thf(1956,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ list_succeeds )
=> ( C @ ( B @ ( A @ append_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:ground:1)') ).
thf(1549,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ '@<_succeeds' ) )
& ( B @ nat_succeeds ) )
=> ( ( A = B )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:axiom:successor)') ).
thf(1554,plain,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ '@<_succeeds' ) )
& ( B @ nat_succeeds ) )
=> ( ( A = B )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@<_succeeds' ) )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:transitive)') ).
thf(1110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@<_succeeds' ) )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( B @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:types:3)') ).
thf(1686,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( B @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ nat_succeeds )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:termination:1)') ).
thf(350,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ nat_succeeds )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(351,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ! [B: $i,C: $i] : ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
inference(miniscope,[status(thm)],[350]) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ plus_terminates ) ) )
| ~ ( A @ nat_succeeds ) ),
inference(cnf,[status(esa)],[351]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( '0'
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id3) ).
thf(1200,plain,
! [A: $i,B: $i] :
( '0'
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( B @ ( A @ same_occ_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:soundness)') ).
thf(977,plain,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( B @ ( A @ same_occ_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ lh @ ( B @ lh @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:lh:leq:second)') ).
thf(1882,plain,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ lh @ ( B @ lh @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(319,axiom,
! [A: $i] :
~ ( ( A @ list_fails )
& ( A @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id38) ).
thf(1939,plain,
! [A: $i] :
~ ( ( A @ list_fails )
& ( A @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( A @ ( '0' @ s @ '@*' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:one)') ).
thf(873,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( A @ ( '0' @ s @ '@*' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ ( A @ '@+' ) @ ( A @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus:first)_011') ).
thf(878,plain,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ ( A @ '@+' ) @ ( A @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ length_fails ) )
<=> ( ( ( B != '0' )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_fails ) )
| ( B
!= ( E @ s ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id80) ).
thf(1437,plain,
! [A: $i,B: $i] :
( ( ( ( ( B != '0' )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_fails ) )
| ( B
!= ( E @ s ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ length_fails ) ) )
& ( ( B @ ( A @ length_fails ) )
=> ( ( ( B != '0' )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_fails ) )
| ( B
!= ( E @ s ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ nat_fails )
<=> ( ( A != '0' )
& ! [B: $i] :
( ( B @ nat_fails )
| ( A
!= ( B @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id107) ).
thf(1041,plain,
! [A: $i] :
( ( ( ( A != '0' )
& ! [B: $i] :
( ( B @ nat_fails )
| ( A
!= ( B @ s ) ) ) )
=> ( A @ nat_fails ) )
& ( ( A @ nat_fails )
=> ( ( A != '0' )
& ! [B: $i] :
( ( B @ nat_fails )
| ( A
!= ( B @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(150,axiom,
'0' @ gr,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id10) ).
thf(1173,plain,
'0' @ gr,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times_fails ) ) )
<=> ( ( ( C != '0' )
| ( A != '0' ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) )
| ( A
!= ( D @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id95) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C != '0' )
| ( A != '0' ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) )
| ( A
!= ( D @ s ) ) ) )
=> ( C @ ( B @ ( A @ times_fails ) ) ) )
& ( ( C @ ( B @ ( A @ times_fails ) ) )
=> ( ( ( C != '0' )
| ( A != '0' ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) )
| ( A
!= ( D @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1300,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( ( C != '0' )
| ( A != '0' ) )
& ! [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) ) )
| ( A
!= ( D @ s ) ) ) )
=> ( C @ ( B @ ( A @ times_fails ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times_fails ) ) )
=> ( ( ( C != '0' )
| ( A != '0' ) )
& ! [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) ) )
| ( A
!= ( D @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1299]) ).
thf(1301,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ ( F @ times_fails ) ) )
| ( H = '0' )
| ( H @ ( F @ sk104 ) ) )
& ( ( H @ ( G @ ( F @ times_fails ) ) )
| ( F = '0' )
| ( H @ ( F @ sk104 ) ) )
& ( ( H @ ( G @ ( F @ times_fails ) ) )
| ~ ( H @ ( F @ sk104 ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk106 ) ) @ ( G @ plus_fails ) ) ) )
& ( ( H @ ( G @ ( F @ times_fails ) ) )
| ~ ( H @ ( F @ sk104 ) )
| ~ ( F @ ( G @ ( H @ sk106 ) ) @ ( G @ ( F @ ( G @ ( H @ sk105 ) ) @ times_fails ) ) ) )
& ( ( H @ ( G @ ( F @ times_fails ) ) )
| ~ ( H @ ( F @ sk104 ) )
| ( F
= ( F @ ( G @ ( H @ sk105 ) ) @ s ) ) )
& ( ( C != '0' )
| ( A != '0' )
| ~ ( C @ ( B @ ( A @ times_fails ) ) ) )
& ( ( C @ ( E @ ( B @ plus_fails ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) )
| ( A
!= ( D @ s ) )
| ~ ( C @ ( B @ ( A @ times_fails ) ) ) ) ),
inference(cnf,[status(esa)],[1300]) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ( C != '0' )
| ( A != '0' )
| ~ ( C @ ( B @ ( A @ times_fails ) ) ) ),
inference(cnfConj,[status(thm)],[1301]) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ times_fails ) ) )
| ( C != '0' )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[1305]) ).
thf(1310,plain,
! [A: $i] :
~ ( '0' @ ( A @ ( '0' @ times_fails ) ) ),
inference(simp,[status(thm)],[1309]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( C @ ( B @ ( A @ member2_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member2:termination)') ).
thf(1735,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( C @ ( B @ ( A @ member2_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(299,axiom,
( ! [A: $i] :
( ( ( A = nil )
| ? [B: $i,C: $i] :
( ( ( C @ rev @ rev )
= C )
& ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) )
=> ( ( A @ rev @ rev )
= A ) )
=> ! [A: $i] :
( ( A @ list_succeeds )
=> ( ( A @ rev @ rev )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(1867,plain,
( ! [A: $i] :
( ( ( A = nil )
| ? [B: $i,C: $i] :
( ( ( C @ rev @ rev )
= C )
& ( C @ list_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) )
=> ( ( A @ rev @ rev )
= A ) )
=> ! [A: $i] :
( ( A @ list_succeeds )
=> ( ( A @ rev @ rev )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@<_succeeds' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:less:transitive)') ).
thf(1327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@<_succeeds' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_succeeds ) ) )
=> ( ( B @ ( A @ rev @ '**' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(a_reverse:n_reverse)') ).
thf(1761,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_succeeds ) ) )
=> ( ( B @ ( A @ rev @ '**' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ delete_fails ) ) )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id30) ).
thf(1063,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ delete_fails ) ) )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ '@=<_fails' ) )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( A @ ( B @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:failure)') ).
thf(538,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ '@=<_fails' ) )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( A @ ( B @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_terminates ) ) )
=> ( ( C @ ( B @ ( A @ delete_fails ) ) )
| ( C @ ( B @ ( A @ delete_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id31) ).
thf(930,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_terminates ) ) )
=> ( ( C @ ( B @ ( A @ delete_fails ) ) )
| ( C @ ( B @ ( A @ delete_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( C @ ( B @ '@=<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@*' ) @ ( B @ ( A @ '@*' ) @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:leq:second)') ).
thf(829,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( C @ ( B @ '@=<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@*' ) @ ( B @ ( A @ '@*' ) @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ cons ) )
= ( D @ ( C @ cons ) ) )
=> ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id8) ).
thf(1001,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ cons ) )
= ( D @ ( C @ cons ) ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(144,axiom,
! [A: $i] :
( '0'
!= ( A @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id1) ).
thf(1127,plain,
! [A: $i] :
( '0'
!= ( A @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ member_succeeds ) )
& ( D @ ( C @ ( A @ delete_succeeds ) ) ) )
=> ( ( B = A )
| ( D @ ( B @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:member:1)') ).
thf(1391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ member_succeeds ) )
& ( D @ ( C @ ( A @ delete_succeeds ) ) ) )
=> ( ( B = A )
| ( D @ ( B @ member_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(283,axiom,
( ( nil @ rev )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(rev:nil)') ).
thf(1802,plain,
( ( nil @ rev )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1803,plain,
( ( nil @ rev )
= nil ),
inference(lifteq,[status(thm)],[1802]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ length_succeeds ) )
& ( B @ ( A @ length_succeeds ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(length:uniqueness)') ).
thf(1518,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ length_succeeds ) )
& ( B @ ( A @ length_succeeds ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id7) ).
thf(1254,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(342,axiom,
! [A: $i] : ( nil @ ( A @ cons ) @ list_succeeds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(list:1)') ).
thf(2020,plain,
! [A: $i] : ( nil @ ( A @ cons ) @ list_succeeds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( C @ ( B @ ( A @ '@*' ) @ '@*' ) )
= ( C @ ( B @ '@*' ) @ ( A @ '@*' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:associative)') ).
thf(417,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( C @ ( B @ ( A @ '@*' ) @ '@*' ) )
= ( C @ ( B @ '@*' ) @ ( A @ '@*' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ ( nil @ '**' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:nil)') ).
thf(1529,plain,
! [A: $i] :
( ( A @ ( nil @ '**' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( nil @ ( C @ cons ) @ ( B @ cons ) @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ cons ) @ ( C @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(rev:3)') ).
thf(1967,plain,
! [A: $i,B: $i,C: $i] :
( ( nil @ ( C @ cons ) @ ( B @ cons ) @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ cons ) @ ( C @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ list_succeeds )
=> ( C @ ( B @ ( A @ append_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:termination:1)') ).
thf(1792,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ list_succeeds )
=> ( C @ ( B @ ( A @ append_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ list_fails )
<=> ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id89) ).
thf(785,plain,
! [A: $i] :
( ( ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ list_fails ) )
& ( ( A @ list_fails )
=> ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ '**' ) @ ( A @ sub ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:app:1)') ).
thf(1860,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ '**' ) @ ( A @ sub ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( A @ s )
= ( B @ s ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id4) ).
thf(542,plain,
! [A: $i,B: $i] :
( ( ( A @ s )
= ( B @ s ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( ( A @ rev )
= B )
<=> ( B @ ( A @ n_reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rev/1') ).
thf(1832,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( ( B @ ( A @ n_reverse_succeeds ) )
=> ( ( A @ rev )
= B ) )
& ( ( ( A @ rev )
= B )
=> ( B @ ( A @ n_reverse_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_terminates ) ) )
<=> ( ( $true
| ( A != '0' ) )
& $true
& ! [D: $i,E: $i] :
( ( ( ( ( E @ ( B @ ( D @ plus_terminates ) ) )
| ( C
!= ( E @ s ) ) )
& $true )
| ( A
!= ( D @ s ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id99) ).
thf(357,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_terminates ) ) )
| ( C
!= ( E @ s ) )
| ( A
!= ( D @ s ) ) )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ plus_terminates ) ) )
=> ! [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_terminates ) ) )
| ( C
!= ( E @ s ) )
| ( A
!= ( D @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ s @ ( B @ ( A @ occ_succeeds ) ) )
& ( B @ list_succeeds ) )
=> ( B @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:member:success)') ).
thf(1922,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ s @ ( B @ ( A @ occ_succeeds ) ) )
& ( B @ list_succeeds ) )
=> ( B @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ occ ) )
= ( B @ ( C @ occ ) ) )
& ( A @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( B @ ( A @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:permutation)') ).
thf(1892,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ occ ) )
= ( B @ ( C @ occ ) ) )
& ( A @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( B @ ( A @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_fails ) ) )
<=> ( ( ( C != B )
| ( A != '0' ) )
& ! [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_fails ) ) )
| ( C
!= ( E @ s ) )
| ( A
!= ( D @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id98) ).
thf(881,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C != B )
| ( A != '0' ) )
& ! [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_fails ) ) )
| ( C
!= ( E @ s ) )
| ( A
!= ( D @ s ) ) ) )
=> ( C @ ( B @ ( A @ plus_fails ) ) ) )
& ( ( C @ ( B @ ( A @ plus_fails ) ) )
=> ( ( ( C != B )
| ( A != '0' ) )
& ! [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_fails ) ) )
| ( C
!= ( E @ s ) )
| ( A
!= ( D @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( B @ ( A @ reverse_fails ) )
<=> ( B @ ( A @ n_reverse_fails ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(reverse:failure)') ).
thf(1778,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( ( B @ ( A @ n_reverse_fails ) )
=> ( B @ ( A @ reverse_fails ) ) )
& ( ( B @ ( A @ reverse_fails ) )
=> ( B @ ( A @ n_reverse_fails ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( nil @ ( B @ cons ) @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(rev:2)') ).
thf(1811,plain,
! [A: $i,B: $i] :
( ( nil @ ( B @ cons ) @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ list_terminates )
<=> ( $true
& ! [B: $i,C: $i] :
( ( ( C @ list_terminates )
| ( A
!= ( C @ ( B @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id90) ).
thf(623,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( C @ list_terminates )
| ( A
!= ( C @ ( B @ cons ) ) ) )
=> ( A @ list_terminates ) )
& ( ( A @ list_terminates )
=> ! [B: $i,C: $i] :
( ( C @ list_terminates )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ reverse_terminates ) )
<=> ( B @ ( nil @ ( A @ a_reverse_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id57) ).
thf(646,plain,
! [A: $i,B: $i] :
( ( ( B @ ( nil @ ( A @ a_reverse_terminates ) ) )
=> ( B @ ( A @ reverse_terminates ) ) )
& ( ( B @ ( A @ reverse_terminates ) )
=> ( B @ ( nil @ ( A @ a_reverse_terminates ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(296,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ rev @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(rev:types)') ).
thf(1858,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ rev @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_fails ) )
<=> ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ ( E @ permutation_fails ) )
| ( E @ ( A @ ( C @ delete_fails ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id74) ).
thf(514,plain,
! [A: $i,B: $i] :
( ( ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ ( E @ permutation_fails ) )
| ( E @ ( A @ ( C @ delete_fails ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ permutation_fails ) ) )
& ( ( B @ ( A @ permutation_fails ) )
=> ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ ( E @ permutation_fails ) )
| ( E @ ( A @ ( C @ delete_fails ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ cons ) @ ( B @ append_succeeds ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:member)') ).
thf(937,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ cons ) @ ( B @ append_succeeds ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ? [B: $i] : ( B @ ( A @ n_reverse_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(n_reverse:existence)') ).
thf(1677,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ? [B: $i] : ( B @ ( A @ n_reverse_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ ( nil @ permutation_succeeds ) )
=> ( A = nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:nil)') ).
thf(806,plain,
! [A: $i] :
( ( A @ ( nil @ permutation_succeeds ) )
=> ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ nat_succeeds )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:termination:2)') ).
thf(353,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ nat_succeeds )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1042,plain,
( ! [A: $i] :
( ( ( A != '0' )
& ! [B: $i] :
( ( B @ nat_fails )
| ( A
!= ( B @ s ) ) ) )
=> ( A @ nat_fails ) )
& ! [A: $i] :
( ( A @ nat_fails )
=> ( ( A != '0' )
& ! [B: $i] :
( ( B @ nat_fails )
| ( A
!= ( B @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1041]) ).
thf(1043,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ nat_fails )
| ( C = '0' )
| ~ ( C @ sk81 @ nat_fails ) )
& ( ( C @ nat_fails )
| ( C = '0' )
| ( C
= ( C @ sk81 @ s ) ) )
& ( ( A != '0' )
| ~ ( A @ nat_fails ) )
& ( ( B @ nat_fails )
| ( A
!= ( B @ s ) )
| ~ ( A @ nat_fails ) ) ),
inference(cnf,[status(esa)],[1042]) ).
thf(1045,plain,
! [A: $i] :
( ( A != '0' )
| ~ ( A @ nat_fails ) ),
inference(cnfConj,[status(thm)],[1043]) ).
thf(1050,plain,
! [A: $i] :
( ~ ( A @ nat_fails )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[1045]) ).
thf(1051,plain,
~ ( '0' @ nat_fails ),
inference(simp,[status(thm)],[1050]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ nat_list_succeeds )
<=> ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ nat_list_succeeds )
& ( B @ nat_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id91) ).
thf(1374,plain,
! [A: $i] :
( ( ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ nat_list_succeeds )
& ( B @ nat_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ nat_list_succeeds ) )
& ( ( A @ nat_list_succeeds )
=> ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ nat_list_succeeds )
& ( B @ nat_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1375,plain,
( ! [A: $i] :
( ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ nat_list_succeeds )
& ( B @ nat_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ nat_list_succeeds ) )
& ! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( ( A = nil )
| ? [B: $i,C: $i] :
( ( C @ nat_list_succeeds )
& ( B @ nat_succeeds )
& ( A
= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1374]) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ nat_list_succeeds )
| ( B != nil ) )
& ( ( B @ nat_list_succeeds )
| ~ ( D @ nat_list_succeeds )
| ~ ( C @ nat_succeeds )
| ( B
!= ( D @ ( C @ cons ) ) ) )
& ( ( A = nil )
| ( A @ sk119 @ nat_list_succeeds )
| ~ ( A @ nat_list_succeeds ) )
& ( ( A = nil )
| ( A @ sk118 @ nat_succeeds )
| ~ ( A @ nat_list_succeeds ) )
& ( ( A = nil )
| ( A
= ( A @ sk119 @ ( A @ sk118 @ cons ) ) )
| ~ ( A @ nat_list_succeeds ) ) ),
inference(cnf,[status(esa)],[1375]) ).
thf(1379,plain,
! [A: $i] :
( ( A @ nat_list_succeeds )
| ( A != nil ) ),
inference(cnfConj,[status(thm)],[1376]) ).
thf(1382,plain,
! [A: $i] :
( ( A @ nat_list_succeeds )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[1379]) ).
thf(1383,plain,
nil @ nat_list_succeeds,
inference(simp,[status(thm)],[1382]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ '@+' ) )
= ( A @ ( B @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:commutative)') ).
thf(1020,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ '@+' ) )
= ( A @ ( B @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:termination:3)') ).
thf(348,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( C @ ( B @ ( A @ plus_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr ) )
<=> ( B @ ( A @ cons ) @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id13) ).
thf(602,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ cons ) @ gr )
=> ( ( B @ gr )
& ( A @ gr ) ) )
& ( ( ( B @ gr )
& ( A @ gr ) )
=> ( B @ ( A @ cons ) @ gr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) )
=> ( C @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(a_reverse:types:2)') ).
thf(1843,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) )
=> ( C @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( A @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:ground:1)') ).
thf(397,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( A @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_succeeds ) ) )
=> ? [D: $i,E: $i] :
( ( C
= ( E @ ( D @ '**' ) ) )
& ( B
= ( E @ ( A @ cons ) @ ( D @ '**' ) ) )
& ( D @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:app:2)') ).
thf(1928,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_succeeds ) ) )
=> ? [D: $i,E: $i] :
( ( C
= ( E @ ( D @ '**' ) ) )
& ( B
= ( E @ ( A @ cons ) @ ( D @ '**' ) ) )
& ( D @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member2_terminates ) ) )
<=> ( ( B @ ( A @ member_terminates ) )
& ( C @ ( A @ member_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id63) ).
thf(634,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ member_terminates ) )
& ( C @ ( A @ member_terminates ) ) )
=> ( C @ ( B @ ( A @ member2_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ member2_terminates ) ) )
=> ( ( B @ ( A @ member_terminates ) )
& ( C @ ( A @ member_terminates ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ list_succeeds )
=> ( C @ ( B @ ( A @ delete_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:termination:2)') ).
thf(1886,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ list_succeeds )
=> ( C @ ( B @ ( A @ delete_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(190,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ same_occ_fails ) )
& ( B @ ( A @ same_occ_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id26) ).
thf(1394,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ same_occ_fails ) )
& ( B @ ( A @ same_occ_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(211,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ '@<_fails' ) )
& ( B @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id48) ).
thf(1526,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ '@<_fails' ) )
& ( B @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( A @ ( B @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:symmetric)') ).
thf(660,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( A @ ( B @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_succeeds ) )
=> ? [C: $i] : ( C @ ( B @ ( A @ delete_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:member:existence)') ).
thf(1405,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ member_succeeds ) )
=> ? [C: $i] : ( C @ ( B @ ( A @ delete_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_terminates' ) )
<=> ( $true
& ! [C: $i,D: $i] :
( ( ( ( ( D @ ( C @ '@=<_terminates' ) )
| ( B
!= ( D @ s ) ) )
& $true )
| ( A
!= ( C @ s ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id102) ).
thf(428,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( D @ ( C @ '@=<_terminates' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) )
=> ( B @ ( A @ '@=<_terminates' ) ) )
& ( ( B @ ( A @ '@=<_terminates' ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ '@=<_terminates' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ length_terminates ) )
=> ( ( B @ ( A @ length_fails ) )
| ( B @ ( A @ length_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id33) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ length_terminates ) )
=> ( ( B @ ( A @ length_fails ) )
| ( B @ ( A @ length_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( A @ ( '0' @ '@*' ) )
= '0' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:zero)') ).
thf(1521,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( A @ ( '0' @ '@*' ) )
= '0' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ( A @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:types)') ).
thf(507,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ( A @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(245,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(rev:1)') ).
thf(1697,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ same_occ_terminates ) )
<=> ( ( B @ gr )
& ( A @ gr )
& ( B @ ( A @ not_same_occ_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id72) ).
thf(1242,plain,
! [A: $i,B: $i] :
( ( ( ( B @ gr )
& ( A @ gr )
& ( B @ ( A @ not_same_occ_terminates ) ) )
=> ( B @ ( A @ same_occ_terminates ) ) )
& ( ( B @ ( A @ same_occ_terminates ) )
=> ( ( B @ gr )
& ( A @ gr )
& ( B @ ( A @ not_same_occ_terminates ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ list_succeeds )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( C
!= ( D @ ( A @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:cons:different)') ).
thf(1863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ list_succeeds )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( C
!= ( D @ ( A @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member2_succeeds ) ) )
<=> ( ( B @ ( A @ member_succeeds ) )
| ( C @ ( A @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id61) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ member_succeeds ) )
| ( C @ ( A @ member_succeeds ) ) )
=> ( C @ ( B @ ( A @ member2_succeeds ) ) ) )
& ( ( C @ ( B @ ( A @ member2_succeeds ) ) )
=> ( ( B @ ( A @ member_succeeds ) )
| ( C @ ( A @ member_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@=<_succeeds' ) )
& ( C @ ( A @ '@<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:less:leq)') ).
thf(512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@=<_succeeds' ) )
& ( C @ ( A @ '@<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( ( C @ ( B @ ( A @ cons ) @ '**' ) )
= ( C @ ( B @ '**' ) @ ( A @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:cons)') ).
thf(1691,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( ( C @ ( B @ ( A @ cons ) @ '**' ) )
= ( C @ ( B @ '**' ) @ ( A @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ same_occ_succeeds ) )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ! [C: $i] :
( ( A @ ( C @ occ ) )
= ( B @ ( C @ occ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(same_occ:success)') ).
thf(1915,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ same_occ_succeeds ) )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ! [C: $i] :
( ( A @ ( C @ occ ) )
= ( B @ ( C @ occ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_succeeds ) ) )
=> ( B @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:member:2)') ).
thf(714,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_succeeds ) ) )
=> ( B @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( ( B @ lh )
= ( C @ lh @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:length)') ).
thf(2000,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( ( B @ lh )
= ( C @ lh @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ ( A @ '@<_terminates' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:termination:1)') ).
thf(1223,plain,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ ( A @ '@<_terminates' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_terminates ) )
<=> ( ( $true
| ( A != nil ) )
& $true
& ! [C: $i,D: $i,E: $i] :
( ( ( ( ( D @ ( E @ permutation_terminates ) )
| ( E @ ( A @ ( C @ delete_fails ) ) ) )
& ( E @ ( A @ ( C @ delete_terminates ) ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id75) ).
thf(952,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( ( ( D @ ( E @ permutation_terminates ) )
| ( E @ ( A @ ( C @ delete_fails ) ) ) )
& ( E @ ( A @ ( C @ delete_terminates ) ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) )
=> ( B @ ( A @ permutation_terminates ) ) )
& ( ( B @ ( A @ permutation_terminates ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( ( D @ ( E @ permutation_terminates ) )
| ( E @ ( A @ ( C @ delete_fails ) ) ) )
& ( E @ ( A @ ( C @ delete_terminates ) ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_succeeds ) ) )
<=> ( ( B
= ( C @ ( A @ cons ) ) )
| ? [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_succeeds ) ) )
& ( C
= ( F @ ( D @ cons ) ) )
& ( B
= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id76) ).
thf(1580,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
= ( C @ ( A @ cons ) ) )
| ? [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_succeeds ) ) )
& ( C
= ( F @ ( D @ cons ) ) )
& ( B
= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
& ( ( C @ ( B @ ( A @ delete_succeeds ) ) )
=> ( ( B
= ( C @ ( A @ cons ) ) )
| ? [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_succeeds ) ) )
& ( C
= ( F @ ( D @ cons ) ) )
& ( B
= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
<=> ( ( A = '0' )
| ? [C: $i,D: $i] :
( ( D @ ( C @ '@=<_succeeds' ) )
& ( B
= ( D @ s ) )
& ( A
= ( C @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id100) ).
thf(1174,plain,
! [A: $i,B: $i] :
( ( ( ( A = '0' )
| ? [C: $i,D: $i] :
( ( D @ ( C @ '@=<_succeeds' ) )
& ( B
= ( D @ s ) )
& ( A
= ( C @ s ) ) ) )
=> ( B @ ( A @ '@=<_succeeds' ) ) )
& ( ( B @ ( A @ '@=<_succeeds' ) )
=> ( ( A = '0' )
| ? [C: $i,D: $i] :
( ( D @ ( C @ '@=<_succeeds' ) )
& ( B
= ( D @ s ) )
& ( A
= ( C @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(160,axiom,
! [A: $i] :
( ( nil @ ( A @ occ ) )
= '0' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:nil)') ).
thf(1217,plain,
! [A: $i] :
( ( nil @ ( A @ occ ) )
= '0' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(67,axiom,
! [A: $i] :
( ( ( A != '0' )
& ( A @ nat_succeeds ) )
=> ( A @ ( '0' @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:different:zero)') ).
thf(693,plain,
! [A: $i] :
( ( ( A != '0' )
& ( A @ nat_succeeds ) )
=> ( A @ ( '0' @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ member_succeeds ) )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:member:1)') ).
thf(1370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ member_succeeds ) )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( ( ( B @ ( A @ occ ) )
= C )
<=> ( C @ ( B @ ( A @ occ_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','occ/2') ).
thf(1900,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( ( ( C @ ( B @ ( A @ occ_succeeds ) ) )
=> ( ( B @ ( A @ occ ) )
= C ) )
& ( ( ( B @ ( A @ occ ) )
= C )
=> ( C @ ( B @ ( A @ occ_succeeds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ member_succeeds ) )
& ( B @ list_succeeds ) )
=> ? [C: $i] :
( ( B @ ( A @ occ ) )
= ( C @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member:occ:success)') ).
thf(1723,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ member_succeeds ) )
& ( B @ list_succeeds ) )
=> ? [C: $i] :
( ( B @ ( A @ occ ) )
= ( C @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(143,axiom,
! [A: $i] :
( nil
!= ( A @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id5) ).
thf(1123,plain,
! [A: $i] :
( nil
!= ( A @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ plus_terminates ) ) )
| ~ ( C @ ( B @ ( A @ plus_succeeds ) ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_succeeds ) ) )
<=> ( ( ( C = B )
& ( A = nil ) )
| ? [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_succeeds ) ) )
& ( A
= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id52) ).
thf(561,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C = B )
& ( A = nil ) )
| ? [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_succeeds ) ) )
& ( A
= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) )
& ( ( C @ ( B @ ( A @ a_reverse_succeeds ) ) )
=> ( ( ( C = B )
& ( A = nil ) )
| ? [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_succeeds ) ) )
& ( A
= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
<=> ( ( A = '0' )
| ? [B: $i] :
( ( B @ nat_succeeds )
& ( A
= ( B @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id106) ).
thf(1654,plain,
! [A: $i] :
( ( ( ( A = '0' )
| ? [B: $i] :
( ( B @ nat_succeeds )
& ( A
= ( B @ s ) ) ) )
=> ( A @ nat_succeeds ) )
& ( ( A @ nat_succeeds )
=> ( ( A = '0' )
| ? [B: $i] :
( ( B @ nat_succeeds )
& ( A
= ( B @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1655,plain,
( ! [A: $i] :
( ( ( A = '0' )
| ? [B: $i] :
( ( B @ nat_succeeds )
& ( A
= ( B @ s ) ) ) )
=> ( A @ nat_succeeds ) )
& ! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( A = '0' )
| ? [B: $i] :
( ( B @ nat_succeeds )
& ( A
= ( B @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1654]) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ nat_succeeds )
| ( B != '0' ) )
& ( ( B @ nat_succeeds )
| ~ ( C @ nat_succeeds )
| ( B
!= ( C @ s ) ) )
& ( ( A = '0' )
| ( A @ sk150 @ nat_succeeds )
| ~ ( A @ nat_succeeds ) )
& ( ( A = '0' )
| ( A
= ( A @ sk150 @ s ) )
| ~ ( A @ nat_succeeds ) ) ),
inference(cnf,[status(esa)],[1655]) ).
thf(1660,plain,
! [A: $i] :
( ( A @ nat_succeeds )
| ( A != '0' ) ),
inference(cnfConj,[status(thm)],[1656]) ).
thf(1665,plain,
! [A: $i] :
( ( A @ nat_succeeds )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[1660]) ).
thf(1666,plain,
'0' @ nat_succeeds,
inference(simp,[status(thm)],[1665]) ).
thf(13,axiom,
! [A: $i] :
~ ( ( A @ nat_fails )
& ( A @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id50) ).
thf(390,plain,
! [A: $i] :
~ ( ( A @ nat_fails )
& ( A @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(391,plain,
~ ? [A: $i] :
( ( A @ nat_fails )
& ( A @ nat_succeeds ) ),
inference(miniscope,[status(thm)],[390]) ).
thf(392,plain,
! [A: $i] :
( ~ ( A @ nat_fails )
| ~ ( A @ nat_succeeds ) ),
inference(cnf,[status(esa)],[391]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_succeeds ) ) )
<=> ( ( ( C = '0' )
& ( B = nil ) )
| ? [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_succeeds ) ) )
& ( C
= ( E @ s ) )
& ( B
= ( D @ ( A @ cons ) ) ) )
| ? [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_succeeds ) ) )
& ( A != D )
& ( B
= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id64) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C = '0' )
& ( B = nil ) )
| ? [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_succeeds ) ) )
& ( C
= ( E @ s ) )
& ( B
= ( D @ ( A @ cons ) ) ) )
| ? [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_succeeds ) ) )
& ( A != D )
& ( B
= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ occ_succeeds ) ) ) )
& ( ( C @ ( B @ ( A @ occ_succeeds ) ) )
=> ( ( ( C = '0' )
& ( B = nil ) )
| ? [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_succeeds ) ) )
& ( C
= ( E @ s ) )
& ( B
= ( D @ ( A @ cons ) ) ) )
| ? [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_succeeds ) ) )
& ( A != D )
& ( B
= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
<=> ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_succeeds ) ) )
& ( E @ ( D @ n_reverse_succeeds ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id58) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_succeeds ) ) )
& ( E @ ( D @ n_reverse_succeeds ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ n_reverse_succeeds ) ) )
& ( ( B @ ( A @ n_reverse_succeeds ) )
=> ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_succeeds ) ) )
& ( E @ ( D @ n_reverse_succeeds ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1415,plain,
( ! [A: $i,B: $i] :
( ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i] :
( ? [E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_succeeds ) ) )
& ( E @ ( D @ n_reverse_succeeds ) ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ n_reverse_succeeds ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
=> ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i] :
( ? [E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_succeeds ) ) )
& ( E @ ( D @ n_reverse_succeeds ) ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1414]) ).
thf(1416,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ n_reverse_succeeds ) )
| ( D != nil )
| ( C != nil ) )
& ( ( D @ ( C @ n_reverse_succeeds ) )
| ~ ( D @ ( nil @ ( E @ cons ) @ ( G @ append_succeeds ) ) )
| ~ ( G @ ( F @ n_reverse_succeeds ) )
| ( C
!= ( F @ ( E @ cons ) ) ) )
& ( ( B @ ( A @ sk107 ) )
| ( B @ ( nil @ ( A @ ( B @ sk121 ) @ cons ) @ ( A @ ( B @ sk123 ) @ append_succeeds ) ) )
| ~ ( B @ ( A @ n_reverse_succeeds ) ) )
& ( ( B @ ( A @ sk107 ) )
| ( A @ ( B @ sk123 ) @ ( A @ ( B @ sk122 ) @ n_reverse_succeeds ) )
| ~ ( B @ ( A @ n_reverse_succeeds ) ) )
& ( ( B @ ( A @ sk107 ) )
| ( A
= ( A @ ( B @ sk122 ) @ ( A @ ( B @ sk121 ) @ cons ) ) )
| ~ ( B @ ( A @ n_reverse_succeeds ) ) ) ),
inference(cnf,[status(esa)],[1415]) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
| ( B != nil )
| ( A != nil ) ),
inference(cnfConj,[status(thm)],[1416]) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
| ( B != nil )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[1420]) ).
thf(1423,plain,
nil @ ( nil @ n_reverse_succeeds ),
inference(simp,[status(thm)],[1422]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ nat_succeeds )
=> ( ( ( B @ ( A @ '@+' ) )
= C )
<=> ( C @ ( B @ ( A @ plus_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','(@+)/2') ).
thf(1602,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ nat_succeeds )
=> ( ( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( ( B @ ( A @ '@+' ) )
= C ) )
& ( ( ( B @ ( A @ '@+' ) )
= C )
=> ( C @ ( B @ ( A @ plus_succeeds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( A @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(nat_list:list)') ).
thf(1920,plain,
! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( A @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(323,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ? [B: $i] :
( ! [C: $i] :
( ( C @ ( A @ n_reverse_succeeds ) )
=> ( B = C ) )
& ( B @ ( A @ n_reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(n_reverse:function)') ).
thf(1951,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ? [B: $i] :
( ! [C: $i] :
( ( C @ ( A @ n_reverse_succeeds ) )
=> ( B = C ) )
& ( B @ ( A @ n_reverse_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( nil @ ( B @ cons ) @ ( A @ '**' ) @ rev )
= ( A @ rev @ ( B @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(rev:app)') ).
thf(1888,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( nil @ ( B @ cons ) @ ( A @ '**' ) @ rev )
= ( A @ rev @ ( B @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_terminates' ) )
<=> ( ! [C: $i] :
( ( $true
| ( A != '0' ) )
& $true )
& ! [C: $i,D: $i] :
( ( ( ( ( D @ ( C @ '@<_terminates' ) )
| ( B
!= ( D @ s ) ) )
& $true )
| ( A
!= ( C @ s ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id105) ).
thf(493,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( D @ ( C @ '@<_terminates' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) )
=> ( B @ ( A @ '@<_terminates' ) ) )
& ( ( B @ ( A @ '@<_terminates' ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ '@<_terminates' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ gr )
& ( B @ gr )
& ( C @ ( B @ ( A @ member2_succeeds ) ) ) )
=> ( A @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member2:ground)') ).
thf(1291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ gr )
& ( B @ gr )
& ( C @ ( B @ ( A @ member2_succeeds ) ) ) )
=> ( A @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_succeeds ) ) )
=> ( A @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:types:1)') ).
thf(1740,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_succeeds ) ) )
=> ( A @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ nat_list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( ( C @ nat_list_succeeds )
& ( A @ nat_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:nat_list)') ).
thf(1106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ nat_list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( ( C @ nat_list_succeeds )
& ( A @ nat_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@+' ) @ ( B @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus:second)_012') ).
thf(682,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@+' ) @ ( B @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( B @ nat_succeeds )
=> ( B @ ( A @ '@<_terminates' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:termination:2)') ).
thf(1195,plain,
! [A: $i,B: $i] :
( ( B @ nat_succeeds )
=> ( B @ ( A @ '@<_terminates' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ '@+' ) )
= ( C @ ( B @ '@+' ) ) )
& ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:injective:first)') ).
thf(1407,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ '@+' ) )
= ( C @ ( B @ '@+' ) ) )
& ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ ( A @ '@*' ) @ '@+' ) )
= ( B @ s @ ( A @ '@*' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:successor)_004') ).
thf(1402,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ ( A @ '@*' ) @ '@+' ) )
= ( B @ s @ ( A @ '@*' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ nat_list_fails )
<=> ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id92) ).
thf(578,plain,
! [A: $i] :
( ( ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ nat_list_fails ) )
& ( ( A @ nat_list_fails )
=> ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ occ_succeeds ) ) )
& ( C @ ( B @ ( A @ occ_succeeds ) ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:uniqueness)') ).
thf(1089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ occ_succeeds ) ) )
& ( C @ ( B @ ( A @ occ_succeeds ) ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ occ ) )
= ( C @ s ) )
& ( B @ list_succeeds ) )
=> ( B @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:member:success)_019') ).
thf(1983,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ occ ) )
= ( C @ s ) )
& ( B @ list_succeeds ) )
=> ( B @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( B @ ( A @ cons ) @ lh @ ( B @ lh @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:cons:leq)') ).
thf(1772,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( B @ ( A @ cons ) @ lh @ ( B @ lh @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( ( B @ list_succeeds )
& ( A @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:types:4)') ).
thf(1804,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( ( B @ list_succeeds )
& ( A @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_terminates ) )
=> ( ( B @ ( A @ member_fails ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id37) ).
thf(1121,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ member_terminates ) )
=> ( ( B @ ( A @ member_fails ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( A @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(nat_list:ground)') ).
thf(725,plain,
! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( A @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ not_same_occ_fails ) )
<=> ! [C: $i,D: $i,E: $i] :
( ( D = E )
| ( E @ ( B @ ( C @ occ_fails ) ) )
| ( D @ ( A @ ( C @ occ_fails ) ) )
| ( B @ ( A @ ( C @ member2_fails ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id68) ).
thf(403,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( D = E )
| ( E @ ( B @ ( C @ occ_fails ) ) )
| ( D @ ( A @ ( C @ occ_fails ) ) )
| ( B @ ( A @ ( C @ member2_fails ) ) ) )
=> ( B @ ( A @ not_same_occ_fails ) ) )
& ( ( B @ ( A @ not_same_occ_fails ) )
=> ! [C: $i,D: $i,E: $i] :
( ( D = E )
| ( E @ ( B @ ( C @ occ_fails ) ) )
| ( D @ ( A @ ( C @ occ_fails ) ) )
| ( B @ ( A @ ( C @ member2_fails ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ '**' ) @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:types:2)') ).
thf(1672,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ '**' ) @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member2_terminates ) ) )
=> ( ( C @ ( B @ ( A @ member2_fails ) ) )
| ( C @ ( B @ ( A @ member2_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id21) ).
thf(388,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member2_terminates ) ) )
=> ( ( C @ ( B @ ( A @ member2_fails ) ) )
| ( C @ ( B @ ( A @ member2_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:ground:1)') ).
thf(1719,plain,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(51,axiom,
! [A: $i] : ( A @ ( A @ sub ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:reflexive)') ).
thf(610,plain,
! [A: $i] : ( A @ ( A @ sub ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ not_same_occ_terminates ) )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( ( ( ( ( ( E @ gr )
& ( D @ gr )
& $true )
| ( E @ ( B @ ( C @ occ_fails ) ) ) )
& ( E @ ( B @ ( C @ occ_terminates ) ) ) )
| ( D @ ( A @ ( C @ occ_fails ) ) ) )
& ( D @ ( A @ ( C @ occ_terminates ) ) ) )
| ( B @ ( A @ ( C @ member2_fails ) ) ) )
& ( B @ ( A @ ( C @ member2_terminates ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id69) ).
thf(1350,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( ( ( ( ( ( ( E @ gr )
& ( D @ gr ) )
| ( E @ ( B @ ( C @ occ_fails ) ) ) )
& ( E @ ( B @ ( C @ occ_terminates ) ) ) )
| ( D @ ( A @ ( C @ occ_fails ) ) ) )
& ( D @ ( A @ ( C @ occ_terminates ) ) ) )
| ( B @ ( A @ ( C @ member2_fails ) ) ) )
& ( B @ ( A @ ( C @ member2_terminates ) ) ) )
=> ( B @ ( A @ not_same_occ_terminates ) ) )
& ( ( B @ ( A @ not_same_occ_terminates ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( ( ( ( ( ( E @ gr )
& ( D @ gr ) )
| ( E @ ( B @ ( C @ occ_fails ) ) ) )
& ( E @ ( B @ ( C @ occ_terminates ) ) ) )
| ( D @ ( A @ ( C @ occ_fails ) ) ) )
& ( D @ ( A @ ( C @ occ_terminates ) ) ) )
| ( B @ ( A @ ( C @ member2_fails ) ) ) )
& ( B @ ( A @ ( C @ member2_terminates ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ '**' ) @ ( B @ sub ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:app:2)') ).
thf(1936,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ '**' ) @ ( B @ sub ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( A @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:types)') ).
thf(1540,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( A @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_terminates ) ) )
<=> ( $true
& ! [D: $i,E: $i,F: $i] :
( ( ( ( ( F @ ( E @ ( A @ delete_terminates ) ) )
| ( C
!= ( F @ ( D @ cons ) ) ) )
& $true )
| ( B
!= ( E @ ( D @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id78) ).
thf(1006,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_terminates ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( B
!= ( E @ ( D @ cons ) ) ) )
=> ( C @ ( B @ ( A @ delete_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ delete_terminates ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_terminates ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ member2_fails ) ) )
& ( C @ ( B @ ( A @ member2_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id20) ).
thf(420,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ member2_fails ) ) )
& ( C @ ( B @ ( A @ member2_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(141,axiom,
'0' != nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id2) ).
thf(1118,plain,
'0' != nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ append_fails ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id34) ).
thf(857,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ append_fails ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( B @ s @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:weakening)') ).
thf(1397,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( B @ s @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ nat_list_terminates )
<=> ( $true
& ! [B: $i,C: $i] :
( ( ( ( ( C @ nat_list_terminates )
| ( B @ nat_fails ) )
& ( B @ nat_terminates ) )
| ( A
!= ( C @ ( B @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id93) ).
thf(471,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( ( C @ nat_list_terminates )
| ( B @ nat_fails ) )
& ( B @ nat_terminates ) )
| ( A
!= ( C @ ( B @ cons ) ) ) )
=> ( A @ nat_list_terminates ) )
& ( ( A @ nat_list_terminates )
=> ! [B: $i,C: $i] :
( ( ( ( C @ nat_list_terminates )
| ( B @ nat_fails ) )
& ( B @ nat_terminates ) )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
<=> ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( D @ ( E @ permutation_succeeds ) )
& ( E @ ( A @ ( C @ delete_succeeds ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id73) ).
thf(1329,plain,
! [A: $i,B: $i] :
( ( ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( D @ ( E @ permutation_succeeds ) )
& ( E @ ( A @ ( C @ delete_succeeds ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ permutation_succeeds ) ) )
& ( ( B @ ( A @ permutation_succeeds ) )
=> ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( D @ ( E @ permutation_succeeds ) )
& ( E @ ( A @ ( C @ delete_succeeds ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_fails ) ) )
<=> ( ( ( C != '0' )
| ( B != nil ) )
& ! [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_fails ) ) )
| ( C
!= ( E @ s ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_fails ) ) )
| ( A = D )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id65) ).
thf(1134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C != '0' )
| ( B != nil ) )
& ! [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_fails ) ) )
| ( C
!= ( E @ s ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_fails ) ) )
| ( A = D )
| ( B
!= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ occ_fails ) ) ) )
& ( ( C @ ( B @ ( A @ occ_fails ) ) )
=> ( ( ( C != '0' )
| ( B != nil ) )
& ! [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_fails ) ) )
| ( C
!= ( E @ s ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_fails ) ) )
| ( A = D )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1135,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( ( C != '0' )
| ( B != nil ) )
& ! [D: $i] :
( ! [E: $i] :
( ( E @ ( D @ ( A @ occ_fails ) ) )
| ( C
!= ( E @ s ) ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_fails ) ) )
| ( A = D )
| ( B
!= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ occ_fails ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_fails ) ) )
=> ( ( ( C != '0' )
| ( B != nil ) )
& ! [D: $i] :
( ! [E: $i] :
( ( E @ ( D @ ( A @ occ_fails ) ) )
| ( C
!= ( E @ s ) ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( A @ occ_fails ) ) )
| ( A = D )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1134]) ).
thf(1136,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ( J = '0' )
| ( J @ ( I @ sk93 ) )
| ( J @ ( H @ ( I @ sk90 ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ( I = nil )
| ( J @ ( I @ sk93 ) )
| ( J @ ( H @ ( I @ sk90 ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ~ ( J @ ( I @ sk93 ) )
| ~ ( H @ ( I @ ( J @ sk95 ) ) @ ( H @ ( I @ ( J @ sk94 ) ) @ ( H @ occ_fails ) ) )
| ( J @ ( H @ ( I @ sk90 ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ~ ( J @ ( I @ sk93 ) )
| ( J
= ( H @ ( I @ ( J @ sk95 ) ) @ s ) )
| ( J @ ( H @ ( I @ sk90 ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ~ ( J @ ( I @ sk93 ) )
| ( I
= ( H @ ( I @ ( J @ sk94 ) ) @ ( H @ cons ) ) )
| ( J @ ( H @ ( I @ sk90 ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ~ ( J @ ( H @ ( I @ sk90 ) ) )
| ~ ( J @ ( H @ ( I @ ( J @ sk92 ) ) @ ( H @ occ_fails ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ~ ( J @ ( H @ ( I @ sk90 ) ) )
| ( H
!= ( H @ ( I @ ( J @ sk91 ) ) ) ) )
& ( ( J @ ( I @ ( H @ occ_fails ) ) )
| ~ ( J @ ( H @ ( I @ sk90 ) ) )
| ( I
= ( H @ ( I @ ( J @ sk92 ) ) @ ( H @ ( I @ ( J @ sk91 ) ) @ cons ) ) ) )
& ( ( C != '0' )
| ( B != nil )
| ~ ( C @ ( B @ ( A @ occ_fails ) ) ) )
& ( ( G @ ( F @ ( A @ occ_fails ) ) )
| ( C
!= ( G @ s ) )
| ( B
!= ( F @ ( A @ cons ) ) )
| ~ ( C @ ( B @ ( A @ occ_fails ) ) ) )
& ( ( C @ ( E @ ( A @ occ_fails ) ) )
| ( A = D )
| ( B
!= ( E @ ( D @ cons ) ) )
| ~ ( C @ ( B @ ( A @ occ_fails ) ) ) ) ),
inference(cnf,[status(esa)],[1135]) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ( C != '0' )
| ( B != nil )
| ~ ( C @ ( B @ ( A @ occ_fails ) ) ) ),
inference(cnfConj,[status(thm)],[1136]) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ occ_fails ) ) )
| ( C != '0' )
| ( B != nil ) ),
inference(lifteq,[status(thm)],[1145]) ).
thf(1160,plain,
! [A: $i] :
~ ( '0' @ ( nil @ ( A @ occ_fails ) ) ),
inference(simp,[status(thm)],[1159]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ? [C: $i] :
( ( C @ s @ ( A @ '@+' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus)_008') ).
thf(686,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ? [C: $i] :
( ( C @ s @ ( A @ '@+' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( B @ ( A @ occ ) @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:types)_017') ).
thf(1700,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( B @ ( A @ occ ) @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
& ( C @ ( B @ member_succeeds ) )
& ( D @ ( C @ ( A @ delete_succeeds ) ) ) )
=> ( D @ ( B @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:member:different)') ).
thf(1214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
& ( C @ ( B @ member_succeeds ) )
& ( D @ ( C @ ( A @ delete_succeeds ) ) ) )
=> ( D @ ( B @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ reverse_succeeds ) )
<=> ( B @ ( nil @ ( A @ a_reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id55) ).
thf(547,plain,
! [A: $i,B: $i] :
( ( ( B @ ( nil @ ( A @ a_reverse_succeeds ) ) )
=> ( B @ ( A @ reverse_succeeds ) ) )
& ( ( B @ ( A @ reverse_succeeds ) )
=> ( B @ ( nil @ ( A @ a_reverse_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( ( C @ ( B @ '**' ) @ ( A @ occ ) )
= ( C @ ( A @ occ ) @ ( B @ ( A @ occ ) @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:app)') ).
thf(1964,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( ( C @ ( B @ '**' ) @ ( A @ occ ) )
= ( C @ ( A @ occ ) @ ( B @ ( A @ occ ) @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] : ( nil @ ( C @ cons ) @ ( B @ cons ) @ ( A @ cons ) @ list_succeeds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(list:3)') ).
thf(1942,plain,
! [A: $i,B: $i,C: $i] : ( nil @ ( C @ cons ) @ ( B @ cons ) @ ( A @ cons ) @ list_succeeds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(515,plain,
( ! [A: $i,B: $i] :
( ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ permutation_fails ) )
| ( E @ ( A @ ( C @ delete_fails ) ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ permutation_fails ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ permutation_fails ) )
=> ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ permutation_fails ) )
| ( E @ ( A @ ( C @ delete_fails ) ) ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[514]) ).
thf(516,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ permutation_fails ) )
| ( G = nil )
| ( G @ ( F @ sk19 ) ) )
& ( ( G @ ( F @ permutation_fails ) )
| ( F = nil )
| ( G @ ( F @ sk19 ) ) )
& ( ( G @ ( F @ permutation_fails ) )
| ~ ( G @ ( F @ sk19 ) )
| ~ ( F @ ( G @ sk21 ) @ ( F @ ( G @ sk22 ) @ permutation_fails ) ) )
& ( ( G @ ( F @ permutation_fails ) )
| ~ ( G @ ( F @ sk19 ) )
| ~ ( F @ ( G @ sk22 ) @ ( F @ ( F @ ( G @ sk20 ) @ delete_fails ) ) ) )
& ( ( G @ ( F @ permutation_fails ) )
| ~ ( G @ ( F @ sk19 ) )
| ( G
= ( F @ ( G @ sk21 ) @ ( F @ ( G @ sk20 ) @ cons ) ) ) )
& ( ( B != nil )
| ( A != nil )
| ~ ( B @ ( A @ permutation_fails ) ) )
& ( ( D @ ( E @ permutation_fails ) )
| ( E @ ( A @ ( C @ delete_fails ) ) )
| ( B
!= ( D @ ( C @ cons ) ) )
| ~ ( B @ ( A @ permutation_fails ) ) ) ),
inference(cnf,[status(esa)],[515]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != nil )
| ~ ( B @ ( A @ permutation_fails ) ) ),
inference(cnfConj,[status(thm)],[516]) ).
thf(525,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ permutation_fails ) )
| ( B != nil )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[523]) ).
thf(526,plain,
~ ( nil @ ( nil @ permutation_fails ) ),
inference(simp,[status(thm)],[525]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ s @ ( A @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:one:success)') ).
thf(1039,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ s @ ( A @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ member_succeeds ) )
& ( C @ ( B @ permutation_succeeds ) ) )
=> ( C @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:member)') ).
thf(970,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ member_succeeds ) )
& ( C @ ( B @ permutation_succeeds ) ) )
=> ( C @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
<=> ( ( ( C = B )
& ( A = '0' ) )
| ? [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_succeeds ) ) )
& ( C
= ( E @ s ) )
& ( A
= ( D @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id97) ).
thf(1266,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C = B )
& ( A = '0' ) )
| ? [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_succeeds ) ) )
& ( C
= ( E @ s ) )
& ( A
= ( D @ s ) ) ) )
=> ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
& ( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( ( ( C = B )
& ( A = '0' ) )
| ? [D: $i,E: $i] :
( ( E @ ( B @ ( D @ plus_succeeds ) ) )
& ( C
= ( E @ s ) )
& ( A
= ( D @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@+' ) @ ( C @ ( A @ '@+' ) @ '@<_succeeds' ) )
& ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:inverse)_013') ).
thf(1131,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@+' ) @ ( C @ ( A @ '@+' ) @ '@<_succeeds' ) )
& ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( C @ ( B @ '@<_succeeds' ) )
& ( A != '0' )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@*' ) @ ( B @ ( A @ '@*' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:less:second)') ).
thf(1192,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( C @ ( B @ '@<_succeeds' ) )
& ( A != '0' )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@*' ) @ ( B @ ( A @ '@*' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ s @ '@*' ) )
= ( B @ ( A @ '@*' ) @ ( B @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:successor)') ).
thf(1060,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ s @ '@*' ) )
= ( B @ ( A @ '@*' ) @ ( B @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ cons ) @ ( A @ occ ) )
= ( B @ ( A @ occ ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:cons:eq)') ).
thf(2006,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ cons ) @ ( A @ occ ) )
= ( B @ ( A @ occ ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( B @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:types:2)') ).
thf(1799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( B @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(199,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ length_fails ) )
& ( B @ ( A @ length_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id32) ).
thf(1429,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ length_fails ) )
& ( B @ ( A @ length_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@*' ) @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:types)') ).
thf(371,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@*' ) @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ list_succeeds )
=> ( B @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(list:cons)') ).
thf(1759,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ list_succeeds )
=> ( B @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ? [C: $i] : ( B @ ( C @ ( A @ plus_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus)') ).
thf(393,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ? [C: $i] : ( B @ ( C @ ( A @ plus_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(139,axiom,
! [A: $i,B: $i] : ( B @ ( A @ cons ) @ ( B @ sub ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:cons)') ).
thf(1114,plain,
! [A: $i,B: $i] : ( B @ ( A @ cons ) @ ( B @ sub ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( A @ ( B @ '**' ) @ ( B @ ( A @ '**' ) @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:app:commutative)') ).
thf(1776,plain,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( A @ ( B @ '**' ) @ ( B @ ( A @ '**' ) @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
& ( D @ ( B @ cons ) @ ( A @ member_succeeds ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member:cons)') ).
thf(1263,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A != B )
& ( C @ ( B @ cons ) @ ( A @ member_succeeds ) ) )
=> ( C @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_terminates ) ) )
=> ( ( C @ ( B @ ( A @ append_fails ) ) )
| ( C @ ( B @ ( A @ append_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id35) ).
thf(997,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_terminates ) ) )
=> ( ( C @ ( B @ ( A @ append_fails ) ) )
| ( C @ ( B @ ( A @ append_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ list_terminates ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(list:termination)') ).
thf(1695,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ list_terminates ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ length_succeeds ) )
=> ( B @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(length:ground)') ).
thf(1170,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ length_succeeds ) )
=> ( B @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@<_succeeds' ) )
& ( C @ ( A @ '@=<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:leq:less)') ).
thf(1286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@<_succeeds' ) )
& ( C @ ( A @ '@=<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ lh @ ( A @ lh @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:lh:leq:first)') ).
thf(1895,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ lh @ ( A @ lh @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_terminates ) )
=> ( ( B @ ( A @ permutation_fails ) )
| ( B @ ( A @ permutation_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id29) ).
thf(662,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_terminates ) )
=> ( ( B @ ( A @ permutation_fails ) )
| ( B @ ( A @ permutation_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
& ( D @ ( C @ ( A @ delete_succeeds ) ) )
& ( C @ list_succeeds ) )
=> ( ( C @ ( B @ occ ) )
= ( D @ ( B @ occ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:occ:diff)') ).
thf(1814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != B )
& ( D @ ( C @ ( A @ delete_succeeds ) ) )
& ( C @ list_succeeds ) )
=> ( ( C @ ( B @ occ ) )
= ( D @ ( B @ occ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ occ_fails ) ) )
& ( C @ ( B @ ( A @ occ_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id22) ).
thf(1086,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ occ_fails ) ) )
& ( C @ ( B @ ( A @ occ_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ s @ ( A @ '@+' ) )
= ( B @ ( A @ s @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:successor)_002') ).
thf(558,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ s @ ( A @ '@+' ) )
= ( B @ ( A @ s @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_fails ) )
<=> ( ! [C: $i] :
( B
!= ( C @ ( A @ cons ) ) )
& ! [C: $i,D: $i] :
( ( D @ ( A @ member_fails ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id86) ).
thf(1071,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( B
!= ( C @ ( A @ cons ) ) )
& ! [C: $i,D: $i] :
( ( D @ ( A @ member_fails ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ member_fails ) ) )
& ( ( B @ ( A @ member_fails ) )
=> ( ! [C: $i] :
( B
!= ( C @ ( A @ cons ) ) )
& ! [C: $i,D: $i] :
( ( D @ ( A @ member_fails ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ cons ) )
= ( D @ ( C @ cons ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id9) ).
thf(1648,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ cons ) )
= ( D @ ( C @ cons ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( A @ gr )
& ( B @ ( A @ n_reverse_succeeds ) ) )
=> ( B @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(n_reverse:ground)') ).
thf(750,plain,
! [A: $i,B: $i] :
( ( ( A @ gr )
& ( B @ ( A @ n_reverse_succeeds ) ) )
=> ( B @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_succeeds ) ) )
=> ( A @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(a_reverse:types:1)') ).
thf(1764,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_succeeds ) ) )
=> ( A @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( ( B @ ( A @ '**' ) @ lh )
= ( B @ lh @ ( A @ lh @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:lh)') ).
thf(1754,plain,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( ( B @ ( A @ '**' ) @ lh )
= ( B @ lh @ ( A @ lh @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(2026,plain,
( ( ( sk1 @ rev @ rev )
!= ( nil @ rev ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[1803,347]) ).
thf(2028,plain,
( ( ( sk1 @ rev )
!= nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2030,plain,
( ( ( sk1 @ rev )
!= ( nil @ rev ) )
| ( nil != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[1803,2028]) ).
thf(2031,plain,
( ( ( sk1 @ rev )
!= ( nil @ rev ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[2030]) ).
thf(2032,plain,
( ( sk1 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2033,plain,
sk1 != nil,
inference(simp,[status(thm)],[2032]) ).
thf(1218,plain,
! [A: $i] :
( ( nil @ ( A @ occ ) )
= '0' ),
inference(cnf,[status(esa)],[1217]) ).
thf(1219,plain,
! [A: $i] :
( ( nil @ ( A @ occ ) )
= '0' ),
inference(lifteq,[status(thm)],[1218]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( ( B @ ( A @ s @ '@+' ) )
= ( B @ ( A @ '@+' ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:successor)') ).
thf(1483,plain,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( ( B @ ( A @ s @ '@+' ) )
= ( B @ ( A @ '@+' ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ s @ ( C @ ( B @ cons ) @ lh @ ( A @ lh @ '@+' ) @ '@<_succeeds' ) )
& ( C @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( D @ ( C @ lh @ ( A @ lh @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:cons:second)') ).
thf(1747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ s @ ( C @ ( B @ cons ) @ lh @ ( A @ lh @ '@+' ) @ '@<_succeeds' ) )
& ( C @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( D @ ( C @ lh @ ( A @ lh @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:uniqueness)') ).
thf(1595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@=<_succeeds' ) )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:leq:transitive)') ).
thf(689,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@=<_succeeds' ) )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( B @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:types:3)') ).
thf(444,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( B @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ nat_terminates )
=> ( ( A @ nat_fails )
| ( A @ nat_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id51) ).
thf(375,plain,
! [A: $i] :
( ( A @ nat_terminates )
=> ( ( A @ nat_fails )
| ( A @ nat_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ plus_succeeds ) ) )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:uniqueness)') ).
thf(423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ plus_succeeds ) ) )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:types:1)') ).
thf(1884,plain,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ? [C: $i] : ( C @ ( B @ ( A @ occ_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:existence)') ).
thf(1752,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ? [C: $i] : ( C @ ( B @ ( A @ occ_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_succeeds ) ) )
=> ( ( C @ nat_succeeds )
& ( B @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:types)') ).
thf(2016,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_succeeds ) ) )
=> ( ( C @ nat_succeeds )
& ( B @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ same_occ_succeeds ) )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:completeness)_018') ).
thf(1795,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ same_occ_succeeds ) )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( ( A @ lh )
= ( B @ lh ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:length)') ).
thf(1226,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( ( A @ lh )
= ( B @ lh ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( C @ ( B @ ( A @ '@+' ) @ '@*' ) )
= ( C @ ( B @ '@*' ) @ ( C @ ( A @ '@*' ) @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:times:distributive)') ).
thf(904,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( C @ ( B @ ( A @ '@+' ) @ '@*' ) )
= ( C @ ( B @ '@*' ) @ ( C @ ( A @ '@*' ) @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ sub ) )
=> ( C @ ( A @ cons ) @ ( B @ ( A @ cons ) @ sub ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:cons:both)') ).
thf(975,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ sub ) )
=> ( C @ ( A @ cons ) @ ( B @ ( A @ cons ) @ sub ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( A @ nat_list_terminates ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(nat_list:termination)') ).
thf(1615,plain,
! [A: $i] :
( ( A @ nat_list_succeeds )
=> ( A @ nat_list_terminates ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( A @ member_succeeds ) ) )
=> ( C @ ( B @ '**' ) @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:member:2)') ).
thf(1784,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( A @ member_succeeds ) ) )
=> ( C @ ( B @ '**' ) @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(188,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ nat_terminates ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(nat:termination)') ).
thf(1389,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ nat_terminates ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( B @ ( A @ member_succeeds ) ) )
=> ( A @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member:ground)') ).
thf(641,plain,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( B @ ( A @ member_succeeds ) ) )
=> ( A @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ length_succeeds ) )
<=> ( ( ( B = '0' )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_succeeds ) )
& ( B
= ( E @ s ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id79) ).
thf(696,plain,
! [A: $i,B: $i] :
( ( ( ( ( B = '0' )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_succeeds ) )
& ( B
= ( E @ s ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ length_succeeds ) ) )
& ( ( B @ ( A @ length_succeeds ) )
=> ( ( ( B = '0' )
& ( A = nil ) )
| ? [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_succeeds ) )
& ( B
= ( E @ s ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(697,plain,
( ! [A: $i,B: $i] :
( ( ( ( B = '0' )
& ( A = nil ) )
| ? [C: $i,D: $i] :
( ? [E: $i] :
( ( E @ ( D @ length_succeeds ) )
& ( B
= ( E @ s ) ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ length_succeeds ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ length_succeeds ) )
=> ( ( ( B = '0' )
& ( A = nil ) )
| ? [C: $i,D: $i] :
( ? [E: $i] :
( ( E @ ( D @ length_succeeds ) )
& ( B
= ( E @ s ) ) )
& ( A
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[696]) ).
thf(698,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ length_succeeds ) )
| ( D != '0' )
| ( C != nil ) )
& ( ( D @ ( C @ length_succeeds ) )
| ~ ( G @ ( F @ length_succeeds ) )
| ( D
!= ( G @ s ) )
| ( C
!= ( F @ ( E @ cons ) ) ) )
& ( ( B = '0' )
| ~ ( B @ ( A @ sk37 ) )
| ~ ( B @ ( A @ length_succeeds ) ) )
& ( ( A = nil )
| ~ ( B @ ( A @ sk37 ) )
| ~ ( B @ ( A @ length_succeeds ) ) )
& ( ( B @ ( A @ sk37 ) )
| ( A @ ( B @ sk40 ) @ ( A @ ( B @ sk39 ) @ length_succeeds ) )
| ~ ( B @ ( A @ length_succeeds ) ) )
& ( ( B @ ( A @ sk37 ) )
| ( B
= ( A @ ( B @ sk40 ) @ s ) )
| ~ ( B @ ( A @ length_succeeds ) ) )
& ( ( B @ ( A @ sk37 ) )
| ( A
= ( A @ ( B @ sk39 ) @ ( A @ ( B @ sk38 ) @ cons ) ) )
| ~ ( B @ ( A @ length_succeeds ) ) ) ),
inference(cnf,[status(esa)],[697]) ).
thf(699,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ length_succeeds ) )
| ( B != '0' )
| ( A != nil ) ),
inference(cnfConj,[status(thm)],[698]) ).
thf(712,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ length_succeeds ) )
| ( B != '0' )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[699]) ).
thf(713,plain,
'0' @ ( nil @ length_succeeds ),
inference(simp,[status(thm)],[712]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ cons ) @ ( B @ ( A @ cons ) @ permutation_succeeds ) )
=> ( C @ ( B @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:cons)') ).
thf(1058,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ cons ) @ ( B @ ( A @ cons ) @ permutation_succeeds ) )
=> ( C @ ( B @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_terminates ) ) )
<=> ( ( $true
| ( A != nil ) )
& $true
& ! [D: $i,E: $i,F: $i] :
( ( ( ( ( F @ ( B @ ( E @ append_terminates ) ) )
| ( C
!= ( F @ ( D @ cons ) ) ) )
& $true )
| ( A
!= ( E @ ( D @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id84) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_terminates ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) )
=> ( C @ ( B @ ( A @ append_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ append_terminates ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_terminates ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ gr )
& ( B @ gr )
& ( B @ list_succeeds ) )
=> ( C @ ( B @ ( A @ occ_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:termination)') ).
thf(1897,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ gr )
& ( B @ gr )
& ( B @ list_succeeds ) )
=> ( C @ ( B @ ( A @ occ_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ member_succeeds ) )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( ( C @ ( A @ member_succeeds ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:member:3)') ).
thf(1258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ member_succeeds ) )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( ( C @ ( A @ member_succeeds ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( B @ '@*' ) @ ( C @ ( A @ '@*' ) @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:leq:first)') ).
thf(540,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( B @ '@*' ) @ ( C @ ( A @ '@*' ) @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ occ ) )
= ( A @ ( C @ occ ) ) )
& ( B @ list_succeeds ) )
=> ( A @ ( B @ permutation_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:completeness)') ).
thf(1786,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ occ ) )
= ( A @ ( C @ occ ) ) )
& ( B @ list_succeeds ) )
=> ( A @ ( B @ permutation_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( '0' @ ( A @ '@+' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:zero)_001') ).
thf(1669,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( '0' @ ( A @ '@+' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_succeeds ) ) )
<=> ( ( ( C = B )
& ( A = nil ) )
| ? [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_succeeds ) ) )
& ( C
= ( F @ ( D @ cons ) ) )
& ( A
= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id82) ).
thf(979,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C = B )
& ( A = nil ) )
| ? [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_succeeds ) ) )
& ( C
= ( F @ ( D @ cons ) ) )
& ( A
= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ append_succeeds ) ) ) )
& ( ( C @ ( B @ ( A @ append_succeeds ) ) )
=> ( ( ( C = B )
& ( A = nil ) )
| ? [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_succeeds ) ) )
& ( C
= ( F @ ( D @ cons ) ) )
& ( A
= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_terminates ) )
=> ( ( B @ ( A @ n_reverse_fails ) )
| ( B @ ( A @ n_reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id19) ).
thf(831,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_terminates ) )
=> ( ( B @ ( A @ n_reverse_fails ) )
| ( B @ ( A @ n_reverse_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_fails' ) )
<=> ( ( A != '0' )
& ! [C: $i,D: $i] :
( ( D @ ( C @ '@=<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id101) ).
thf(1557,plain,
! [A: $i,B: $i] :
( ( ( ( A != '0' )
& ! [C: $i,D: $i] :
( ( D @ ( C @ '@=<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) )
=> ( B @ ( A @ '@=<_fails' ) ) )
& ( ( B @ ( A @ '@=<_fails' ) )
=> ( ( A != '0' )
& ! [C: $i,D: $i] :
( ( D @ ( C @ '@=<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1558,plain,
( ! [A: $i,B: $i] :
( ( ( A != '0' )
& ! [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ '@=<_fails' ) )
| ( B
!= ( D @ s ) ) )
| ( A
!= ( C @ s ) ) ) )
=> ( B @ ( A @ '@=<_fails' ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_fails' ) )
=> ( ( A != '0' )
& ! [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ '@=<_fails' ) )
| ( B
!= ( D @ s ) ) )
| ( A
!= ( C @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1557]) ).
thf(1559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ '@=<_fails' ) )
| ( E = '0' )
| ~ ( E @ ( F @ sk140 ) @ ( E @ ( F @ sk139 ) @ '@=<_fails' ) ) )
& ( ( F @ ( E @ '@=<_fails' ) )
| ( E = '0' )
| ( F
= ( E @ ( F @ sk140 ) @ s ) ) )
& ( ( F @ ( E @ '@=<_fails' ) )
| ( E = '0' )
| ( E
= ( E @ ( F @ sk139 ) @ s ) ) )
& ( ( A != '0' )
| ~ ( B @ ( A @ '@=<_fails' ) ) )
& ( ( D @ ( C @ '@=<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) )
| ~ ( B @ ( A @ '@=<_fails' ) ) ) ),
inference(cnf,[status(esa)],[1558]) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ( A != '0' )
| ~ ( B @ ( A @ '@=<_fails' ) ) ),
inference(cnfConj,[status(thm)],[1559]) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ '@=<_fails' ) )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[1561]) ).
thf(1574,plain,
! [A: $i] :
~ ( A @ ( '0' @ '@=<_fails' ) ),
inference(simp,[status(thm)],[1573]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( B @ '@+' ) @ ( C @ ( A @ '@+' ) @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus:first)') ).
thf(1524,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( B @ '@+' ) @ ( C @ ( A @ '@+' ) @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ nat_terminates )
<=> ( $true
& ! [B: $i] :
( ( ( B @ nat_terminates )
| ( A
!= ( B @ s ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id108) ).
thf(377,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ nat_terminates )
| ( A
!= ( B @ s ) ) )
=> ( A @ nat_terminates ) )
& ( ( A @ nat_terminates )
=> ! [B: $i] :
( ( B @ nat_terminates )
| ( A
!= ( B @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ! [C: $i] :
( ( A @ ( C @ occ ) )
= ( B @ ( C @ occ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:occ)') ).
thf(599,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ! [C: $i] :
( ( A @ ( C @ occ ) )
= ( B @ ( C @ occ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ s @ '@*' ) @ ( B @ ( A @ s @ '@*' ) @ '@=<_succeeds' ) )
& ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:times:inverse)') ).
thf(863,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ s @ '@*' ) @ ( B @ ( A @ s @ '@*' ) @ '@=<_succeeds' ) )
& ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@<_succeeds' ) )
& ( C @ ( A @ '@<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:less:less)') ).
thf(1667,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@<_succeeds' ) )
& ( C @ ( A @ '@<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ not_same_occ_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(not_same_occ:termination)') ).
thf(1877,plain,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ not_same_occ_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:types:2)') ).
thf(1993,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( B @ ( A @ member_succeeds ) ) )
=> ( C @ ( B @ '**' ) @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:member:1)') ).
thf(1909,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( B @ ( A @ member_succeeds ) ) )
=> ( C @ ( B @ '**' ) @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1330,plain,
( ! [A: $i,B: $i] :
( ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i] :
( ? [E: $i] :
( ( D @ ( E @ permutation_succeeds ) )
& ( E @ ( A @ ( C @ delete_succeeds ) ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ permutation_succeeds ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( ( ( B = nil )
& ( A = nil ) )
| ? [C: $i,D: $i] :
( ? [E: $i] :
( ( D @ ( E @ permutation_succeeds ) )
& ( E @ ( A @ ( C @ delete_succeeds ) ) ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1329]) ).
thf(1331,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ permutation_succeeds ) )
| ( D != nil )
| ( C != nil ) )
& ( ( D @ ( C @ permutation_succeeds ) )
| ~ ( F @ ( G @ permutation_succeeds ) )
| ~ ( G @ ( C @ ( E @ delete_succeeds ) ) )
| ( D
!= ( F @ ( E @ cons ) ) ) )
& ( ( B = nil )
| ~ ( B @ ( A @ sk107 ) )
| ~ ( B @ ( A @ permutation_succeeds ) ) )
& ( ( A = nil )
| ~ ( B @ ( A @ sk107 ) )
| ~ ( B @ ( A @ permutation_succeeds ) ) )
& ( ( B @ ( A @ sk107 ) )
| ( A @ ( B @ sk109 ) @ ( A @ ( B @ sk110 ) @ permutation_succeeds ) )
| ~ ( B @ ( A @ permutation_succeeds ) ) )
& ( ( B @ ( A @ sk107 ) )
| ( A @ ( B @ sk110 ) @ ( A @ ( A @ ( B @ sk108 ) @ delete_succeeds ) ) )
| ~ ( B @ ( A @ permutation_succeeds ) ) )
& ( ( B @ ( A @ sk107 ) )
| ( B
= ( A @ ( B @ sk109 ) @ ( A @ ( B @ sk108 ) @ cons ) ) )
| ~ ( B @ ( A @ permutation_succeeds ) ) ) ),
inference(cnf,[status(esa)],[1330]) ).
thf(1336,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ permutation_succeeds ) )
| ( B != nil )
| ( A != nil ) ),
inference(cnfConj,[status(thm)],[1331]) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ permutation_succeeds ) )
| ( B != nil )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[1336]) ).
thf(1344,plain,
nil @ ( nil @ permutation_succeeds ),
inference(simp,[status(thm)],[1343]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ ( A @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:uniqueness:2)') ).
thf(932,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ ( A @ append_succeeds ) ) )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_terminates ) ) )
=> ( ( C @ ( B @ ( A @ occ_fails ) ) )
| ( C @ ( B @ ( A @ occ_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id23) ).
thf(1112,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_terminates ) ) )
=> ( ( C @ ( B @ ( A @ occ_fails ) ) )
| ( C @ ( B @ ( A @ occ_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(345,plain,
sk1 @ list_succeeds,
inference(cnfConj,[status(thm)],[344]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( ( A @ lh )
= B )
<=> ( B @ ( A @ length_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lh/1') ).
thf(1821,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( ( ( B @ ( A @ length_succeeds ) )
=> ( ( A @ lh )
= B ) )
& ( ( ( A @ lh )
= B )
=> ( B @ ( A @ length_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ length_succeeds ) )
=> ( ( B @ nat_succeeds )
& ( A @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(length:types)') ).
thf(1731,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ length_succeeds ) )
=> ( ( B @ nat_succeeds )
& ( A @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_terminates ) )
<=> ( ( $true
| ( A != nil ) )
& $true
& ! [C: $i,D: $i,E: $i] :
( ( ( ( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_terminates ) ) )
| ( E @ ( D @ n_reverse_fails ) ) )
& ( E @ ( D @ n_reverse_terminates ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id60) ).
thf(769,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( ( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_terminates ) ) )
| ( E @ ( D @ n_reverse_fails ) ) )
& ( E @ ( D @ n_reverse_terminates ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) )
=> ( B @ ( A @ n_reverse_terminates ) ) )
& ( ( B @ ( A @ n_reverse_terminates ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_terminates ) ) )
| ( E @ ( D @ n_reverse_fails ) ) )
& ( E @ ( D @ n_reverse_terminates ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_fails' ) )
<=> ( ! [C: $i] :
( ( B
!= ( C @ s ) )
| ( A != '0' ) )
& ! [C: $i,D: $i] :
( ( D @ ( C @ '@<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id104) ).
thf(1460,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( B
!= ( C @ s ) )
| ( A != '0' ) )
& ! [C: $i,D: $i] :
( ( D @ ( C @ '@<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) )
=> ( B @ ( A @ '@<_fails' ) ) )
& ( ( B @ ( A @ '@<_fails' ) )
=> ( ! [C: $i] :
( ( B
!= ( C @ s ) )
| ( A != '0' ) )
& ! [C: $i,D: $i] :
( ( D @ ( C @ '@<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ s @ ( C @ lh @ ( B @ ( A @ cons ) @ lh @ '@+' ) @ '@<_succeeds' ) )
& ( C @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( D @ ( C @ lh @ ( B @ lh @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:cons:first)') ).
thf(1841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ s @ ( C @ lh @ ( B @ ( A @ cons ) @ lh @ '@+' ) @ '@<_succeeds' ) )
& ( C @ list_succeeds )
& ( B @ list_succeeds ) )
=> ( D @ ( C @ lh @ ( B @ lh @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(85,axiom,
( ( nil @ lh )
= '0' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:nil)') ).
thf(827,plain,
( ( nil @ lh )
= '0' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ '@=<_succeeds' ) )
| ( B @ ( A @ '@=<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:totality)') ).
thf(1435,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ '@=<_succeeds' ) )
| ( B @ ( A @ '@=<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ gr )
<=> ( A @ s @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id11) ).
thf(851,plain,
! [A: $i] :
( ( ( A @ s @ gr )
=> ( A @ gr ) )
& ( ( A @ gr )
=> ( A @ s @ gr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(130,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ member_fails ) )
& ( B @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id36) ).
thf(1066,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ member_fails ) )
& ( B @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ '@+' ) @ ( C @ '@*' ) )
= ( B @ ( C @ '@*' ) @ ( A @ ( C @ '@*' ) @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:times:distributive)_006') ).
thf(868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ '@+' ) @ ( C @ '@*' ) )
= ( B @ ( C @ '@*' ) @ ( A @ ( C @ '@*' ) @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( ( B @ lh @ ( A @ lh @ '@+' ) )
= ( C @ lh ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:lh)') ).
thf(1726,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( ( B @ lh @ ( A @ lh @ '@+' ) )
= ( C @ lh ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@=<_succeeds' ) )
& ( C @ ( A @ '@=<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:leq:leq)') ).
thf(1250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ nat_succeeds )
& ( D @ ( B @ '@=<_succeeds' ) )
& ( C @ ( A @ '@=<_succeeds' ) ) )
=> ( D @ ( C @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(322,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ occ ) )
= '0' )
& ( A @ list_succeeds ) )
=> ( A = nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:zero)') ).
thf(1948,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ occ ) )
= '0' )
& ( A @ list_succeeds ) )
=> ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ '@*' ) )
= ( A @ ( B @ '@*' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:commutative)') ).
thf(490,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( B @ ( A @ '@*' ) )
= ( A @ ( B @ '@*' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ lh @ ( B @ lh @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:lh:leq:second)') ).
thf(1809,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( C @ lh @ ( B @ lh @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ gr )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( C @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:ground:2)') ).
thf(426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ gr )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( C @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(579,plain,
( ! [A: $i] :
( ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ nat_list_fails ) )
& ! [A: $i] :
( ( A @ nat_list_fails )
=> ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[578]) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ nat_list_fails )
| ( D = nil )
| ~ ( D @ sk27 @ nat_list_fails ) )
& ( ( D @ nat_list_fails )
| ( D = nil )
| ~ ( D @ sk26 @ nat_fails ) )
& ( ( D @ nat_list_fails )
| ( D = nil )
| ( D
= ( D @ sk27 @ ( D @ sk26 @ cons ) ) ) )
& ( ( A != nil )
| ~ ( A @ nat_list_fails ) )
& ( ( C @ nat_list_fails )
| ( B @ nat_fails )
| ( A
!= ( C @ ( B @ cons ) ) )
| ~ ( A @ nat_list_fails ) ) ),
inference(cnf,[status(esa)],[579]) ).
thf(583,plain,
! [A: $i] :
( ( A != nil )
| ~ ( A @ nat_list_fails ) ),
inference(cnfConj,[status(thm)],[580]) ).
thf(588,plain,
! [A: $i] :
( ~ ( A @ nat_list_fails )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[583]) ).
thf(589,plain,
~ ( nil @ nat_list_fails ),
inference(simp,[status(thm)],[588]) ).
thf(786,plain,
( ! [A: $i] :
( ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) )
=> ( A @ list_fails ) )
& ! [A: $i] :
( ( A @ list_fails )
=> ( ( A != nil )
& ! [B: $i,C: $i] :
( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[785]) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ list_fails )
| ( D = nil )
| ~ ( D @ sk50 @ list_fails ) )
& ( ( D @ list_fails )
| ( D = nil )
| ( D
= ( D @ sk50 @ ( D @ sk49 @ cons ) ) ) )
& ( ( A != nil )
| ~ ( A @ list_fails ) )
& ( ( C @ list_fails )
| ( A
!= ( C @ ( B @ cons ) ) )
| ~ ( A @ list_fails ) ) ),
inference(cnf,[status(esa)],[786]) ).
thf(789,plain,
! [A: $i] :
( ( A != nil )
| ~ ( A @ list_fails ) ),
inference(cnfConj,[status(thm)],[787]) ).
thf(794,plain,
! [A: $i] :
( ~ ( A @ list_fails )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[789]) ).
thf(795,plain,
~ ( nil @ list_fails ),
inference(simp,[status(thm)],[794]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ list_terminates )
=> ( ( A @ list_fails )
| ( A @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id39) ).
thf(1684,plain,
! [A: $i] :
( ( A @ list_terminates )
=> ( ( A @ list_fails )
| ( A @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ list_succeeds )
=> ( C @ ( B @ ( A @ a_reverse_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(a_reverse:termination)') ).
thf(1990,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ list_succeeds )
=> ( C @ ( B @ ( A @ a_reverse_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member2_fails ) ) )
<=> ( ( B @ ( A @ member_fails ) )
& ( C @ ( A @ member_fails ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id62) ).
thf(939,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ member_fails ) )
& ( C @ ( A @ member_fails ) ) )
=> ( C @ ( B @ ( A @ member2_fails ) ) ) )
& ( ( C @ ( B @ ( A @ member2_fails ) ) )
=> ( ( B @ ( A @ member_fails ) )
& ( C @ ( A @ member_fails ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ member_succeeds ) )
& ( D @ ( C @ ( A @ delete_succeeds ) ) ) )
=> ( C @ ( B @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:member:3)') ).
thf(553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ member_succeeds ) )
& ( D @ ( C @ ( A @ delete_succeeds ) ) ) )
=> ( C @ ( B @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ same_occ_terminates ) )
=> ( ( B @ ( A @ same_occ_fails ) )
| ( B @ ( A @ same_occ_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id27) ).
thf(968,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ same_occ_terminates ) )
=> ( ( B @ ( A @ same_occ_fails ) )
| ( B @ ( A @ same_occ_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ? [C: $i] :
( B
= ( C @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:successor)') ).
thf(1551,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ? [C: $i] :
( B
= ( C @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ plus_fails ) ) )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id44) ).
thf(487,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ plus_fails ) ) )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ permutation_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:termination)_016') ).
thf(1958,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ permutation_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_terminates ) ) )
=> ( ( C @ ( B @ ( A @ plus_fails ) ) )
| ( C @ ( B @ ( A @ plus_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id45) ).
thf(355,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_terminates ) ) )
=> ( ( C @ ( B @ ( A @ plus_fails ) ) )
| ( C @ ( B @ ( A @ plus_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ list_succeeds )
=> ( ( ( B @ ( A @ '**' ) )
= C )
<=> ( C @ ( B @ ( A @ append_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','(**)/2') ).
thf(1845,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ list_succeeds )
=> ( ( ( C @ ( B @ ( A @ append_succeeds ) ) )
=> ( ( B @ ( A @ '**' ) )
= C ) )
& ( ( ( B @ ( A @ '**' ) )
= C )
=> ( C @ ( B @ ( A @ append_succeeds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( C @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:types:1)') ).
thf(1770,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( C @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) )
=> ( B @ list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(a_reverse:types:3)') ).
thf(1961,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ list_succeeds )
& ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) )
=> ( B @ list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ s )
!= ( C @ ( B @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id6) ).
thf(1611,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ s )
!= ( C @ ( B @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( ( C @ ( B @ ( A @ '**' ) @ '**' ) )
= ( C @ ( B @ '**' ) @ ( A @ '**' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:associative)') ).
thf(1743,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( ( C @ ( B @ ( A @ '**' ) @ '**' ) )
= ( C @ ( B @ '**' ) @ ( A @ '**' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ occ ) )
= ( C @ s ) )
& ( B @ list_succeeds ) )
=> ? [D: $i] : ( D @ ( B @ ( A @ delete_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:successor)') ).
thf(2012,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ occ ) )
= ( C @ s ) )
& ( B @ list_succeeds ) )
=> ? [D: $i] : ( D @ ( B @ ( A @ delete_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ( A @ nat_list_succeeds )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( B @ nat_list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:nat_list)') ).
thf(1252,plain,
! [A: $i,B: $i] :
( ( ( A @ nat_list_succeeds )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( B @ nat_list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( ( A @ gr )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( B @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:ground)') ).
thf(1516,plain,
! [A: $i,B: $i] :
( ( ( A @ gr )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( B @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( B @ ( A @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:leq)') ).
thf(1598,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( B @ ( A @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ ( '0' @ '@+' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:zero)') ).
thf(1432,plain,
! [A: $i] :
( ( A @ ( '0' @ '@+' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1175,plain,
( ! [A: $i,B: $i] :
( ( ( A = '0' )
| ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ '@=<_succeeds' ) )
& ( B
= ( D @ s ) ) )
& ( A
= ( C @ s ) ) ) )
=> ( B @ ( A @ '@=<_succeeds' ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ( ( A = '0' )
| ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ '@=<_succeeds' ) )
& ( B
= ( D @ s ) ) )
& ( A
= ( C @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1174]) ).
thf(1176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ '@=<_succeeds' ) )
| ( C != '0' ) )
& ( ( D @ ( C @ '@=<_succeeds' ) )
| ~ ( F @ ( E @ '@=<_succeeds' ) )
| ( D
!= ( F @ s ) )
| ( C
!= ( E @ s ) ) )
& ( ( A = '0' )
| ( A @ ( B @ sk97 ) @ ( A @ ( B @ sk96 ) @ '@=<_succeeds' ) )
| ~ ( B @ ( A @ '@=<_succeeds' ) ) )
& ( ( A = '0' )
| ( B
= ( A @ ( B @ sk97 ) @ s ) )
| ~ ( B @ ( A @ '@=<_succeeds' ) ) )
& ( ( A = '0' )
| ( A
= ( A @ ( B @ sk96 ) @ s ) )
| ~ ( B @ ( A @ '@=<_succeeds' ) ) ) ),
inference(cnf,[status(esa)],[1175]) ).
thf(1180,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
| ( A != '0' ) ),
inference(cnfConj,[status(thm)],[1176]) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[1180]) ).
thf(1188,plain,
! [A: $i] : ( A @ ( '0' @ '@=<_succeeds' ) ),
inference(simp,[status(thm)],[1187]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( '0' @ ( A @ '@*' ) )
= '0' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:zero)_003') ).
thf(717,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( ( '0' @ ( A @ '@*' ) )
= '0' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(170,axiom,
! [A: $i] : ( A @ ( nil @ sub ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:nil)') ).
thf(1261,plain,
! [A: $i] : ( A @ ( nil @ sub ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1262,plain,
! [A: $i] : ( A @ ( nil @ sub ) ),
inference(cnf,[status(esa)],[1261]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ nat_list_terminates )
=> ( ( A @ nat_list_fails )
| ( A @ nat_list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id41) ).
thf(463,plain,
! [A: $i] :
( ( A @ nat_list_terminates )
=> ( ( A @ nat_list_fails )
| ( A @ nat_list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ same_occ_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(same_occ:termination)') ).
thf(1830,plain,
! [A: $i,B: $i] :
( ( ( B @ gr )
& ( A @ gr )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ same_occ_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:inverse)') ).
thf(1538,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ lh )
= A )
& ( B @ list_succeeds )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ permutation_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:termination)') ).
thf(1679,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ lh )
= A )
& ( B @ list_succeeds )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ permutation_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1128,plain,
~ ? [A: $i] :
( '0'
= ( A @ s ) ),
inference(miniscope,[status(thm)],[1127]) ).
thf(1129,plain,
! [A: $i] :
( '0'
!= ( A @ s ) ),
inference(cnf,[status(esa)],[1128]) ).
thf(1130,plain,
! [A: $i] :
( ( A @ s )
!= '0' ),
inference(lifteq,[status(thm)],[1129]) ).
thf(161,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ n_reverse_fails ) )
& ( B @ ( A @ n_reverse_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id18) ).
thf(1220,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ n_reverse_fails ) )
& ( B @ ( A @ n_reverse_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ append_fails ) ) )
<=> ( ( ( C != B )
| ( A != nil ) )
& ! [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_fails ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id83) ).
thf(907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C != B )
| ( A != nil ) )
& ! [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_fails ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ append_fails ) ) ) )
& ( ( C @ ( B @ ( A @ append_fails ) ) )
=> ( ( ( C != B )
| ( A != nil ) )
& ! [D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( E @ append_fails ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ member_fails ) )
& ( B @ list_succeeds ) )
=> ( ( B @ ( A @ occ ) )
= '0' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:member)') ).
thf(1987,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ member_fails ) )
& ( B @ list_succeeds ) )
=> ( ( B @ ( A @ occ ) )
= '0' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( C @ ( B @ '**' ) @ ( C @ ( A @ cons ) @ ( B @ '**' ) @ ( A @ delete_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:app:1)') ).
thf(1716,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( C @ ( B @ '**' ) @ ( C @ ( A @ cons ) @ ( B @ '**' ) @ ( A @ delete_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ '@<_succeeds' ) )
| ( A = B )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:totality)') ).
thf(1543,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ '@<_succeeds' ) )
| ( A = B )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( B @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( A = nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:equal:nil)') ).
thf(1702,plain,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( B @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
=> ! [C: $i] : ( C @ ( B @ '**' ) @ ( C @ ( A @ a_reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(n_reverse:a_reverse)') ).
thf(1284,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
=> ! [C: $i] : ( C @ ( B @ '**' ) @ ( C @ ( A @ a_reverse_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_fails ) ) )
<=> ( ( ( C != B )
| ( A != nil ) )
& ! [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_fails ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id53) ).
thf(727,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C != B )
| ( A != nil ) )
& ! [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_fails ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ a_reverse_fails ) ) ) )
& ( ( C @ ( B @ ( A @ a_reverse_fails ) ) )
=> ( ( ( C != B )
| ( A != nil ) )
& ! [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_fails ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '**' ) @ ( A @ member_succeeds ) )
& ( B @ list_succeeds ) )
=> ( ( C @ ( A @ member_succeeds ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:member:3)') ).
thf(1797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '**' ) @ ( A @ member_succeeds ) )
& ( B @ list_succeeds ) )
=> ( ( C @ ( A @ member_succeeds ) )
| ( B @ ( A @ member_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ? [C: $i] : ( B @ ( C @ s @ ( A @ plus_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus)') ).
thf(1372,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ? [C: $i] : ( B @ ( C @ s @ ( A @ plus_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_terminates ) )
<=> ( ! [C: $i] : $true
& ! [C: $i,D: $i] :
( ( ( D @ ( A @ member_terminates ) )
| ( B
!= ( D @ ( C @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id87) ).
thf(612,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( D @ ( A @ member_terminates ) )
| ( B
!= ( D @ ( C @ cons ) ) ) )
=> ( B @ ( A @ member_terminates ) ) )
& ( ( B @ ( A @ member_terminates ) )
=> ! [C: $i,D: $i] :
( ( D @ ( A @ member_terminates ) )
| ( B
!= ( D @ ( C @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ gr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(nat:ground)') ).
thf(876,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ gr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ occ_terminates ) ) )
<=> ( ( $true
| ( B != nil ) )
& $true
& ! [D: $i,E: $i] :
( ( ( ( ( E @ ( D @ ( A @ occ_terminates ) ) )
| ( C
!= ( E @ s ) ) )
& $true )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& $true )
& ! [D: $i,E: $i] :
( ( ( ( ( C @ ( E @ ( A @ occ_terminates ) ) )
| ( A = D ) )
& ( D @ gr )
& ( A @ gr )
& $true )
| ( B
!= ( E @ ( D @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id66) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_terminates ) ) )
| ( C
!= ( E @ s ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( C @ ( E @ ( A @ occ_terminates ) ) )
| ( A = D ) )
& ( D @ gr )
& ( A @ gr ) )
| ( B
!= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ occ_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ occ_terminates ) ) )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( A @ occ_terminates ) ) )
| ( C
!= ( E @ s ) )
| ( B
!= ( D @ ( A @ cons ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( C @ ( E @ ( A @ occ_terminates ) ) )
| ( A = D ) )
& ( D @ gr )
& ( A @ gr ) )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ length_terminates ) )
<=> ( ( $true
| ( A != nil ) )
& $true
& ! [C: $i,D: $i,E: $i] :
( ( ( ( ( E @ ( D @ length_terminates ) )
| ( B
!= ( E @ s ) ) )
& $true )
| ( A
!= ( D @ ( C @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id81) ).
thf(1023,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_terminates ) )
| ( B
!= ( E @ s ) )
| ( A
!= ( D @ ( C @ cons ) ) ) )
=> ( B @ ( A @ length_terminates ) ) )
& ( ( B @ ( A @ length_terminates ) )
=> ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ length_terminates ) )
| ( B
!= ( E @ s ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ rev @ '**' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(rev:cons)') ).
thf(1749,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ rev @ '**' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ ( A @ '@<_fails' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:failure)') ).
thf(1427,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ ( A @ '@<_fails' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( A @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:types:1)') ).
thf(465,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_succeeds ) ) )
=> ( A @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ? [B: $i] : ( B @ ( A @ length_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(length:existence)') ).
thf(1918,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ? [B: $i] : ( B @ ( A @ length_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1438,plain,
( ! [A: $i,B: $i] :
( ( ( ( B != '0' )
| ( A != nil ) )
& ! [C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ length_fails ) )
| ( B
!= ( E @ s ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ length_fails ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ length_fails ) )
=> ( ( ( B != '0' )
| ( A != nil ) )
& ! [C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ length_fails ) )
| ( B
!= ( E @ s ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1437]) ).
thf(1439,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ length_fails ) )
| ( G = '0' )
| ( G @ ( F @ sk124 ) ) )
& ( ( G @ ( F @ length_fails ) )
| ( F = nil )
| ( G @ ( F @ sk124 ) ) )
& ( ( G @ ( F @ length_fails ) )
| ~ ( G @ ( F @ sk124 ) )
| ~ ( F @ ( G @ sk127 ) @ ( F @ ( G @ sk126 ) @ length_fails ) ) )
& ( ( G @ ( F @ length_fails ) )
| ~ ( G @ ( F @ sk124 ) )
| ( G
= ( F @ ( G @ sk127 ) @ s ) ) )
& ( ( G @ ( F @ length_fails ) )
| ~ ( G @ ( F @ sk124 ) )
| ( F
= ( F @ ( G @ sk126 ) @ ( F @ ( G @ sk125 ) @ cons ) ) ) )
& ( ( B != '0' )
| ( A != nil )
| ~ ( B @ ( A @ length_fails ) ) )
& ( ( E @ ( D @ length_fails ) )
| ( B
!= ( E @ s ) )
| ( A
!= ( D @ ( C @ cons ) ) )
| ~ ( B @ ( A @ length_fails ) ) ) ),
inference(cnf,[status(esa)],[1438]) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( B != '0' )
| ( A != nil )
| ~ ( B @ ( A @ length_fails ) ) ),
inference(cnfConj,[status(thm)],[1439]) ).
thf(1458,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ length_fails ) )
| ( B != '0' )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[1442]) ).
thf(1459,plain,
~ ( '0' @ ( nil @ length_fails ) ),
inference(simp,[status(thm)],[1458]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_terminates ) ) )
=> ( ( C @ ( B @ ( A @ a_reverse_fails ) ) )
| ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id15) ).
thf(556,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_terminates ) ) )
=> ( ( C @ ( B @ ( A @ a_reverse_fails ) ) )
| ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( ( B @ list_succeeds )
& ( A @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:types)') ).
thf(1817,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ permutation_succeeds ) )
=> ( ( B @ list_succeeds )
& ( A @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ same_occ_succeeds ) )
<=> ( B @ ( A @ not_same_occ_fails ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id70) ).
thf(1321,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ not_same_occ_fails ) )
=> ( B @ ( A @ same_occ_succeeds ) ) )
& ( ( B @ ( A @ same_occ_succeeds ) )
=> ( B @ ( A @ not_same_occ_fails ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1124,plain,
~ ? [A: $i] :
( nil
= ( A @ s ) ),
inference(miniscope,[status(thm)],[1123]) ).
thf(1125,plain,
! [A: $i] :
( nil
!= ( A @ s ) ),
inference(cnf,[status(esa)],[1124]) ).
thf(1126,plain,
! [A: $i] :
( ( A @ s )
!= nil ),
inference(lifteq,[status(thm)],[1125]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ '@+' ) )
= ( C @ ( A @ '@+' ) ) )
& ( A @ nat_succeeds ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:injective:second)') ).
thf(1189,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ '@+' ) )
= ( C @ ( A @ '@+' ) ) )
& ( A @ nat_succeeds ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( ( A = B )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:less)') ).
thf(1575,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( ( A = B )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ lh @ ( A @ lh @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:lh:leq:first)') ).
thf(1998,plain,
! [A: $i,B: $i] :
( ( ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( B @ ( A @ '**' ) @ lh @ ( A @ lh @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( B @ ( A @ member_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member:termination)') ).
thf(1721,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( B @ ( A @ member_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ reverse_terminates ) )
=> ( ( B @ ( A @ reverse_fails ) )
| ( B @ ( A @ reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id17) ).
thf(748,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ reverse_terminates ) )
=> ( ( B @ ( A @ reverse_fails ) )
| ( B @ ( A @ reverse_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(237,axiom,
! [A: $i] :
( ( ( ( A @ lh )
= '0' )
& ( A @ list_succeeds ) )
=> ( A = nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:zero)') ).
thf(1674,plain,
! [A: $i] :
( ( ( ( A @ lh )
= '0' )
& ( A @ list_succeeds ) )
=> ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1461,plain,
( ! [A: $i,B: $i] :
( ( ( ~ ? [C: $i] :
( B
= ( C @ s ) )
| ( A != '0' ) )
& ! [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ '@<_fails' ) )
| ( B
!= ( D @ s ) ) )
| ( A
!= ( C @ s ) ) ) )
=> ( B @ ( A @ '@<_fails' ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ '@<_fails' ) )
=> ( ( ~ ? [C: $i] :
( B
= ( C @ s ) )
| ( A != '0' ) )
& ! [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ '@<_fails' ) )
| ( B
!= ( D @ s ) ) )
| ( A
!= ( C @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1460]) ).
thf(1462,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ '@<_fails' ) )
| ( G
= ( F @ ( G @ sk131 ) @ s ) )
| ( G @ ( F @ sk128 ) ) )
& ( ( G @ ( F @ '@<_fails' ) )
| ( F = '0' )
| ( G @ ( F @ sk128 ) ) )
& ( ( G @ ( F @ '@<_fails' ) )
| ~ ( G @ ( F @ sk128 ) )
| ~ ( F @ ( G @ sk130 ) @ ( F @ ( G @ sk129 ) @ '@<_fails' ) ) )
& ( ( G @ ( F @ '@<_fails' ) )
| ~ ( G @ ( F @ sk128 ) )
| ( G
= ( F @ ( G @ sk130 ) @ s ) ) )
& ( ( G @ ( F @ '@<_fails' ) )
| ~ ( G @ ( F @ sk128 ) )
| ( F
= ( F @ ( G @ sk129 ) @ s ) ) )
& ( ( B
!= ( E @ s ) )
| ( A != '0' )
| ~ ( B @ ( A @ '@<_fails' ) ) )
& ( ( D @ ( C @ '@<_fails' ) )
| ( B
!= ( D @ s ) )
| ( A
!= ( C @ s ) )
| ~ ( B @ ( A @ '@<_fails' ) ) ) ),
inference(cnf,[status(esa)],[1461]) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s ) )
| ( A != '0' )
| ~ ( B @ ( A @ '@<_fails' ) ) ),
inference(cnfConj,[status(thm)],[1462]) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ '@<_fails' ) )
| ( B
!= ( C @ s ) )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[1463]) ).
thf(1481,plain,
! [A: $i] :
~ ( A @ s @ ( '0' @ '@<_fails' ) ),
inference(simp,[status(thm)],[1480]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ gr )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( ( C @ gr )
& ( A @ gr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:ground)') ).
thf(946,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ gr )
& ( C @ ( B @ ( A @ delete_succeeds ) ) ) )
=> ( ( C @ gr )
& ( A @ gr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ sub ) )
<=> ! [C: $i] :
( ( A @ ( C @ member_succeeds ) )
=> ( B @ ( C @ member_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sub/2') ).
thf(652,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member_succeeds ) )
=> ( B @ ( C @ member_succeeds ) ) )
=> ( B @ ( A @ sub ) ) )
& ( ( B @ ( A @ sub ) )
=> ! [C: $i] :
( ( A @ ( C @ member_succeeds ) )
=> ( B @ ( C @ member_succeeds ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ '**' ) @ gr )
& ( A @ list_succeeds ) )
=> ( ( B @ gr )
& ( A @ gr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:ground:2)') ).
thf(1854,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ '**' ) @ gr )
& ( A @ list_succeeds ) )
=> ( ( B @ gr )
& ( A @ gr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ length_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(length:termination)') ).
thf(2009,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ length_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ lh @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:types)') ).
thf(1689,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ lh @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ member_succeeds ) )
& ( C @ ( B @ sub ) ) )
=> ( C @ ( B @ ( A @ cons ) @ sub ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:member)') ).
thf(510,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ member_succeeds ) )
& ( C @ ( B @ sub ) ) )
=> ( C @ ( B @ ( A @ cons ) @ sub ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ gr )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( ( B @ gr )
& ( A @ gr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:ground:2)') ).
thf(1294,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ gr )
& ( C @ ( B @ ( A @ append_succeeds ) ) ) )
=> ( ( B @ gr )
& ( A @ gr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ '**' ) )
= ( C @ ( B @ '**' ) ) )
& ( C @ list_succeeds )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:uniqueness:1)') ).
thf(1706,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ '**' ) )
= ( C @ ( B @ '**' ) ) )
& ( C @ list_succeeds )
& ( B @ list_succeeds )
& ( A @ list_succeeds ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ reverse_succeeds ) )
<=> ( B @ ( A @ n_reverse_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(reverse:success)') ).
thf(763,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ n_reverse_succeeds ) )
=> ( B @ ( A @ reverse_succeeds ) ) )
& ( ( B @ ( A @ reverse_succeeds ) )
=> ( B @ ( A @ n_reverse_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( C @ ( B @ ( A @ '@+' ) @ '@+' ) )
= ( C @ ( B @ '@+' ) @ ( A @ '@+' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:associative)') ).
thf(1513,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( C @ ( B @ ( A @ '@+' ) @ '@+' ) )
= ( C @ ( B @ '@+' ) @ ( A @ '@+' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds )
& ( B @ ( '0' @ '@<_succeeds' ) ) )
=> ( A @ ( B @ '@+' ) @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:first)_010') ).
thf(684,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds )
& ( B @ ( '0' @ '@<_succeeds' ) ) )
=> ( A @ ( B @ '@+' ) @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ s @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:one)') ).
thf(536,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ s @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(81,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ permutation_fails ) )
& ( B @ ( A @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id28) ).
thf(800,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ permutation_fails ) )
& ( B @ ( A @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ member_succeeds ) )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(append:member:2)') ).
thf(1348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ member_succeeds ) )
& ( D @ ( C @ ( B @ append_succeeds ) ) ) )
=> ( D @ ( A @ member_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ '@=<_succeeds' ) )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:leq:total)') ).
thf(999,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( ( A @ ( B @ '@=<_succeeds' ) )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ a_reverse_terminates ) ) )
<=> ( ( $true
| ( A != nil ) )
& $true
& ! [D: $i,E: $i] :
( ( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_terminates ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id54) ).
thf(752,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_terminates ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) )
=> ( C @ ( B @ ( A @ a_reverse_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ a_reverse_terminates ) ) )
=> ! [D: $i,E: $i] :
( ( C @ ( B @ ( D @ cons ) @ ( E @ a_reverse_terminates ) ) )
| ( A
!= ( E @ ( D @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ ( A @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:reflexive)') ).
thf(1774,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ( A @ ( A @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times_terminates ) ) )
<=> ( ( $true
| ( A != '0' ) )
& $true
& ! [D: $i,E: $i] :
( ( ( ( ( C @ ( E @ ( B @ plus_terminates ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) ) )
& ( E @ ( B @ ( D @ times_terminates ) ) ) )
| ( A
!= ( D @ s ) ) )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id96) ).
thf(447,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( ( C @ ( E @ ( B @ plus_terminates ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) ) )
& ( E @ ( B @ ( D @ times_terminates ) ) ) )
| ( A
!= ( D @ s ) ) )
=> ( C @ ( B @ ( A @ times_terminates ) ) ) )
& ( ( C @ ( B @ ( A @ times_terminates ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( C @ ( E @ ( B @ plus_terminates ) ) )
| ( E @ ( B @ ( D @ times_fails ) ) ) )
& ( E @ ( B @ ( D @ times_terminates ) ) ) )
| ( A
!= ( D @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@=<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus:second)') ).
thf(1578,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@=<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@=<_succeeds' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( A @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:transitive)') ).
thf(833,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@=<_succeeds' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( C @ ( A @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_succeeds ) )
<=> ( ? [C: $i] :
( B
= ( C @ ( A @ cons ) ) )
| ? [C: $i,D: $i] :
( ( D @ ( A @ member_succeeds ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id85) ).
thf(1229,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( B
= ( C @ ( A @ cons ) ) )
| ? [C: $i,D: $i] :
( ( D @ ( A @ member_succeeds ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ member_succeeds ) ) )
& ( ( B @ ( A @ member_succeeds ) )
=> ( ? [C: $i] :
( B
= ( C @ ( A @ cons ) ) )
| ? [C: $i,D: $i] :
( ( D @ ( A @ member_succeeds ) )
& ( B
= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ n_reverse_succeeds ) )
& ( B @ ( A @ n_reverse_succeeds ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(n_reverse:uniqueness)') ).
thf(1546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ n_reverse_succeeds ) )
& ( B @ ( A @ n_reverse_succeeds ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(266,axiom,
! [A: $i,B: $i] : ( nil @ ( B @ cons ) @ ( A @ cons ) @ list_succeeds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(list:2)') ).
thf(1757,plain,
! [A: $i,B: $i] : ( nil @ ( B @ cons ) @ ( A @ cons ) @ list_succeeds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ s @ ( A @ '@+' ) @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:second)_009') ).
thf(865,plain,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ s @ ( A @ '@+' ) @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_terminates' ) )
=> ( ( B @ ( A @ '@=<_fails' ) )
| ( B @ ( A @ '@=<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id47) ).
thf(373,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_terminates' ) )
=> ( ( B @ ( A @ '@=<_fails' ) )
| ( B @ ( A @ '@=<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ ( A @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:reflexive)') ).
thf(1116,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ ( A @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( ( ( B @ lh )
= ( A @ s ) )
& ( B @ list_succeeds ) )
=> ? [C: $i,D: $i] :
( B
= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:successor)') ).
thf(2003,plain,
! [A: $i,B: $i] :
( ( ( ( B @ lh )
= ( A @ s ) )
& ( B @ list_succeeds ) )
=> ? [C: $i,D: $i] :
( B
= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( B @ '@+' ) @ ( C @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:first)') ).
thf(950,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ nat_succeeds )
& ( B @ nat_succeeds )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( B @ '@+' ) @ ( C @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_fails ) )
<=> ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id59) ).
thf(835,plain,
! [A: $i,B: $i] :
( ( ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ n_reverse_fails ) ) )
& ( ( B @ ( A @ n_reverse_fails ) )
=> ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i,E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(149,axiom,
nil @ gr,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id12) ).
thf(1172,plain,
nil @ gr,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(828,plain,
( ( nil @ lh )
= '0' ),
inference(lifteq,[status(thm)],[827]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ a_reverse_fails ) ) )
& ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id14) ).
thf(720,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ ( A @ a_reverse_fails ) ) )
& ( C @ ( B @ ( A @ a_reverse_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ sub ) )
& ( B @ ( A @ sub ) ) )
=> ( C @ ( A @ sub ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(sub:transitive)') ).
thf(1346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ sub ) )
& ( B @ ( A @ sub ) ) )
=> ( C @ ( A @ sub ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_succeeds ) )
=> ? [C: $i,D: $i] : ( B @ ( D @ ( A @ cons ) @ ( C @ append_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(member:append)') ).
thf(1056,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ member_succeeds ) )
=> ? [C: $i,D: $i] : ( B @ ( D @ ( A @ cons ) @ ( C @ append_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(278,axiom,
! [A: $i] :
( ( A @ list_succeeds )
=> ( ( nil @ ( A @ '**' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:nil)_015') ).
thf(1789,plain,
! [A: $i] :
( ( A @ list_succeeds )
=> ( ( nil @ ( A @ '**' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ delete_fails ) ) )
<=> ( ( B
!= ( C @ ( A @ cons ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_fails ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id77) ).
thf(664,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
!= ( C @ ( A @ cons ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_fails ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( B
!= ( E @ ( D @ cons ) ) ) ) )
=> ( C @ ( B @ ( A @ delete_fails ) ) ) )
& ( ( C @ ( B @ ( A @ delete_fails ) ) )
=> ( ( B
!= ( C @ ( A @ cons ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ delete_fails ) ) )
| ( C
!= ( F @ ( D @ cons ) ) )
| ( B
!= ( E @ ( D @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(175,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ reverse_fails ) )
& ( B @ ( A @ reverse_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id16) ).
thf(1288,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ reverse_fails ) )
& ( B @ ( A @ reverse_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( C @ ( B @ ( A @ delete_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:termination:1)') ).
thf(1710,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ list_succeeds )
=> ( C @ ( B @ ( A @ delete_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ? [C: $i] : ( C @ ( B @ ( A @ plus_succeeds ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:existence)') ).
thf(400,plain,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ? [C: $i] : ( C @ ( B @ ( A @ plus_succeeds ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ ( A @ times_terminates ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(times:termination)') ).
thf(1197,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ ( A @ times_terminates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ nat_succeeds )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( C @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:types:2)') ).
thf(395,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ nat_succeeds )
& ( C @ ( B @ ( A @ plus_succeeds ) ) ) )
=> ( C @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ ( A @ '@=<_terminates' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:termination:1)') ).
thf(596,plain,
! [A: $i,B: $i] :
( ( A @ nat_succeeds )
=> ( B @ ( A @ '@=<_terminates' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ permutation_succeeds ) )
& ( C @ ( A @ permutation_succeeds ) ) )
=> ( D @ ( C @ '**' ) @ ( B @ ( A @ '**' ) @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:app)') ).
thf(644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ permutation_succeeds ) )
& ( C @ ( A @ permutation_succeeds ) ) )
=> ( D @ ( C @ '**' ) @ ( B @ ( A @ '**' ) @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ s @ ( B @ '@<_succeeds' ) )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:transitive:successor)') ).
thf(723,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ s @ ( B @ '@<_succeeds' ) )
& ( B @ ( A @ '@<_succeeds' ) ) )
=> ( C @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(810,plain,
( ! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( B
= ( C @ s ) )
& ( A = '0' ) )
| ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ '@<_succeeds' ) )
& ( B
= ( D @ s ) ) )
& ( A
= ( C @ s ) ) ) )
=> ( B @ ( A @ '@<_succeeds' ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
=> ( ( ? [C: $i] :
( B
= ( C @ s ) )
& ( A = '0' ) )
| ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ '@<_succeeds' ) )
& ( B
= ( D @ s ) ) )
& ( A
= ( C @ s ) ) ) ) ) ),
inference(miniscope,[status(thm)],[809]) ).
thf(811,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ '@<_succeeds' ) )
| ( D
!= ( G @ s ) )
| ( C != '0' ) )
& ( ( D @ ( C @ '@<_succeeds' ) )
| ~ ( F @ ( E @ '@<_succeeds' ) )
| ( D
!= ( F @ s ) )
| ( C
!= ( E @ s ) ) )
& ( ( B
= ( A @ ( B @ sk54 ) @ s ) )
| ~ ( B @ ( A @ sk51 ) )
| ~ ( B @ ( A @ '@<_succeeds' ) ) )
& ( ( A = '0' )
| ~ ( B @ ( A @ sk51 ) )
| ~ ( B @ ( A @ '@<_succeeds' ) ) )
& ( ( B @ ( A @ sk51 ) )
| ( A @ ( B @ sk53 ) @ ( A @ ( B @ sk52 ) @ '@<_succeeds' ) )
| ~ ( B @ ( A @ '@<_succeeds' ) ) )
& ( ( B @ ( A @ sk51 ) )
| ( B
= ( A @ ( B @ sk53 ) @ s ) )
| ~ ( B @ ( A @ '@<_succeeds' ) ) )
& ( ( B @ ( A @ sk51 ) )
| ( A
= ( A @ ( B @ sk52 ) @ s ) )
| ~ ( B @ ( A @ '@<_succeeds' ) ) ) ),
inference(cnf,[status(esa)],[810]) ).
thf(815,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
| ( B
!= ( C @ s ) )
| ( A != '0' ) ),
inference(cnfConj,[status(thm)],[811]) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ '@<_succeeds' ) )
| ( B
!= ( C @ s ) )
| ( A != '0' ) ),
inference(lifteq,[status(thm)],[815]) ).
thf(822,plain,
! [A: $i] : ( A @ s @ ( '0' @ '@<_succeeds' ) ),
inference(simp,[status(thm)],[821]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A != B )
& ( C @ list_succeeds ) )
=> ( ( C @ ( B @ cons ) @ ( A @ occ ) )
= ( C @ ( A @ occ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(occ:cons:diff)') ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A != B )
& ( C @ list_succeeds ) )
=> ( ( C @ ( B @ cons ) @ ( A @ occ ) )
= ( C @ ( A @ occ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ permutation_succeeds ) )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( C @ ( A @ permutation_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(permutation:transitive)') ).
thf(691,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ permutation_succeeds ) )
& ( B @ ( A @ permutation_succeeds ) ) )
=> ( C @ ( A @ permutation_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_terminates' ) )
=> ( ( B @ ( A @ '@<_fails' ) )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id49) ).
thf(442,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@<_terminates' ) )
=> ( ( B @ ( A @ '@<_fails' ) )
| ( B @ ( A @ '@<_succeeds' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ~ ( A @ ( A @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:strictness)') ).
thf(871,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ~ ( A @ ( A @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ '@=<_succeeds' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:antisymmetric)') ).
thf(1399,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ '@=<_succeeds' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1119,plain,
'0' != nil,
inference(polarity_switch,[status(thm)],[1118]) ).
thf(1120,plain,
nil != '0',
inference(lifteq,[status(thm)],[1119]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ reverse_fails ) )
<=> ( B @ ( nil @ ( A @ a_reverse_fails ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id56) ).
thf(1532,plain,
! [A: $i,B: $i] :
( ( ( B @ ( nil @ ( A @ a_reverse_fails ) ) )
=> ( B @ ( A @ reverse_fails ) ) )
& ( ( B @ ( A @ reverse_fails ) )
=> ( B @ ( nil @ ( A @ a_reverse_fails ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ? [C: $i] :
( ( C @ ( A @ '@+' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus)_007') ).
thf(860,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '@=<_succeeds' ) )
=> ? [C: $i] :
( ( C @ ( A @ '@+' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(836,plain,
( ! [A: $i,B: $i] :
( ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i] :
( ! [E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) )
=> ( B @ ( A @ n_reverse_fails ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_fails ) )
=> ( ( ( B != nil )
| ( A != nil ) )
& ! [C: $i,D: $i] :
( ! [E: $i] :
( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) ) )
| ( A
!= ( D @ ( C @ cons ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[835]) ).
thf(837,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ n_reverse_fails ) )
| ~ ( G @ ( F @ sk19 ) )
| ~ ( G @ ( nil @ ( F @ ( G @ sk55 ) @ cons ) @ ( F @ ( G @ sk57 ) @ append_fails ) ) ) )
& ( ( G @ ( F @ n_reverse_fails ) )
| ~ ( G @ ( F @ sk19 ) )
| ~ ( F @ ( G @ sk57 ) @ ( F @ ( G @ sk56 ) @ n_reverse_fails ) ) )
& ( ( G @ ( F @ n_reverse_fails ) )
| ~ ( G @ ( F @ sk19 ) )
| ( F
= ( F @ ( G @ sk56 ) @ ( F @ ( G @ sk55 ) @ cons ) ) ) )
& ( ( B != nil )
| ( A != nil )
| ~ ( B @ ( A @ n_reverse_fails ) ) )
& ( ( B @ ( nil @ ( C @ cons ) @ ( E @ append_fails ) ) )
| ( E @ ( D @ n_reverse_fails ) )
| ( A
!= ( D @ ( C @ cons ) ) )
| ~ ( B @ ( A @ n_reverse_fails ) ) ) ),
inference(cnf,[status(esa)],[836]) ).
thf(839,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != nil )
| ~ ( B @ ( A @ n_reverse_fails ) ) ),
inference(cnfConj,[status(thm)],[837]) ).
thf(849,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ n_reverse_fails ) )
| ( B != nil )
| ( A != nil ) ),
inference(lifteq,[status(thm)],[839]) ).
thf(850,plain,
~ ( nil @ ( nil @ n_reverse_fails ) ),
inference(simp,[status(thm)],[849]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ n_reverse_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(n_reverse:termination)') ).
thf(1713,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ n_reverse_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(82,axiom,
! [A: $i] :
~ ( ( A @ nat_list_fails )
& ( A @ nat_list_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id40) ).
thf(803,plain,
! [A: $i] :
~ ( ( A @ nat_list_fails )
& ( A @ nat_list_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
=> ( ( B @ list_succeeds )
& ( A @ list_succeeds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(n_reverse:types)') ).
thf(1944,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ n_reverse_succeeds ) )
=> ( ( B @ list_succeeds )
& ( A @ list_succeeds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ plus_terminates ) ) )
| ~ ( C @ nat_succeeds ) ),
inference(cnf,[status(esa)],[353]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:second)') ).
thf(935,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '@<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ reverse_terminates ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(reverse:termination)') ).
thf(1737,plain,
! [A: $i,B: $i] :
( ( A @ list_succeeds )
=> ( B @ ( A @ reverse_terminates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ ( A @ s @ '@=<_fails' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:one:failure)') ).
thf(1037,plain,
! [A: $i] :
( ( A @ nat_succeeds )
=> ( A @ ( A @ s @ '@=<_fails' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@=<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(leq:plus:inverse)') ).
thf(1204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ '@+' ) @ ( B @ ( A @ '@+' ) @ '@=<_succeeds' ) )
& ( A @ nat_succeeds ) )
=> ( C @ ( B @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@+' ) @ nat_succeeds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(plus:types)') ).
thf(1069,plain,
! [A: $i,B: $i] :
( ( ( B @ nat_succeeds )
& ( A @ nat_succeeds ) )
=> ( B @ ( A @ '@+' ) @ nat_succeeds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ cons ) @ lh )
= ( B @ lh @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:cons)') ).
thf(1912,plain,
! [A: $i,B: $i] :
( ( B @ list_succeeds )
=> ( ( B @ ( A @ cons ) @ lh )
= ( B @ lh @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(113,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ '@=<_fails' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id46) ).
thf(972,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ '@=<_fails' ) )
& ( B @ ( A @ '@=<_succeeds' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(20329,plain,
$false,
inference(e,[status(thm)],[809,1879,1411,1168,1767,1995,347,1729,1982,468,1956,1549,1554,1110,1686,352,1200,977,1882,1939,873,878,1437,1041,1173,1310,1735,1867,1327,1761,1063,538,930,829,1001,1127,1391,1803,1518,1254,2020,417,1529,1967,1792,785,1860,542,1832,357,1922,1892,881,1778,1811,623,646,1858,514,937,1677,806,353,1051,1383,1020,348,602,1843,397,1928,634,1886,1394,1526,660,1405,428,1600,1521,507,1697,1242,1863,1206,512,1691,1915,714,2000,1223,952,1580,1174,1217,693,1370,1900,1723,1123,349,561,1666,392,1487,1423,1602,1920,1951,1888,493,1291,1740,1106,682,1195,1407,1402,578,1089,1983,1772,1804,1121,1970,725,403,1672,388,1719,610,1350,1936,1540,1006,420,1118,857,1397,471,1329,1160,686,1700,1214,547,1964,1942,1414,526,1039,970,1266,1131,1192,1060,2006,1799,1429,371,1759,393,1114,1776,1263,997,343,1695,1170,1286,1895,662,1814,1086,558,1071,1648,750,1764,1754,2033,1219,1483,1747,1595,689,444,1374,375,423,1884,1752,2016,1795,1226,904,975,1615,1784,1389,641,713,1058,1092,1897,1258,350,540,1786,1669,979,831,1574,1524,377,599,863,1667,1877,1993,1909,1344,932,1112,345,1557,1821,1731,769,1460,1841,827,1435,851,1066,868,1726,1250,1948,490,1809,426,589,795,1684,1990,939,553,968,1551,1134,487,1958,355,1845,1770,1961,1611,1743,2012,1252,1516,1598,1432,1188,717,1262,463,1830,1538,1679,1130,1220,907,1987,1716,1543,1702,1284,727,1797,1372,612,876,1617,1802,1023,1749,1427,465,1918,1459,556,1817,1321,1654,1126,1189,1575,1998,1721,748,1674,1481,946,652,390,1854,2009,1689,510,1294,1706,763,1513,684,536,800,1348,999,752,1774,447,1578,833,1229,1546,1757,865,373,1116,2003,950,835,1172,828,696,720,1346,1056,1789,664,1288,1710,400,1197,395,1261,596,644,723,822,1925,1299,691,442,871,1399,1120,1532,860,850,1713,803,1944,354,935,1737,1037,1204,1069,1912,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX063+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n013.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 16:45:21 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.83/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.87/1.34 % [INFO] Parsing done (364ms).
% 1.87/1.35 % [INFO] Running in sequential loop mode.
% 2.88/1.73 % [INFO] eprover registered as external prover.
% 2.88/1.74 % [INFO] Scanning for conjecture ...
% 3.08/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 3.61/2.04 % [INFO] Axiom selection finished. Selected 340 axioms (removed 14 axioms).
% 4.42/2.30 % [INFO] Problem is first-order (TPTP FOF).
% 4.42/2.33 % [INFO] Type checking passed.
% 4.42/2.33 % [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 ...
% 66.90/15.79 % External prover 'e' found a proof!
% 66.90/15.79 % [INFO] Killing All external provers ...
% 66.90/15.79 % Time passed: 15254ms (effective reasoning time: 14431ms)
% 66.90/15.79 % 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)>
% 66.90/15.79 % Axioms used in derivation (340): axiom-(member2:ground), id30, id86, id64, id48, axiom-(less:leq:total), axiom-(app:nil)_015, axiom-(plus:injective:second), id9, axiom-(less:leq), corollary-(reverse:termination), id75, id96, axiom-(app:types:1), axiom-(nat_list:ground), theorem-(reverse:failure), axiom-(app:uniqueness:1), id59, axiom-(times:zero), id81, id70, axiom-(sub:app:2), axiom-(leq:plus:inverse), axiom-(app:member:3), axiom-(lh:cons:second), axiom-(plus:zero)_001, axiom-(nat_list:termination), axiom-(plus:successor)_002, id41, axiom-(lh:types), axiom-(delete:app:2), axiom-(append:uniqueness:2), id34, axiom-(less:transitive), axiom-(delete:termination:1), axiom-(app:lh), id92, axiom-(leq:failure), axiom-(member:cons), axiom-(permutation:nil), corollary-(rev:types), axiom-(append:types:1), axiom-(less:plus:first)_010, axiom-(sub:reflexive), id21, id10, lemma-(a_reverse:termination), id5, id85, axiom-(leq:plus:first)_011, axiom-(delete:member:2), axiom-(append:member:2), id74, id45, id97, id56, axiom-(app:ground:1), axiom-(less:totality), id91, axiom-(plus:ground:1), axiom-(less:weakening), id63, axiom-(times:commutative), id13, id51, lemma-(n_reverse:uniqueness), id37, id19, lemma-(n_reverse:a_reverse), axiom-(same_occ:success), axiom-(times:zero)_003, axiom-(delete:types:1), axiom-(delete:member:different), id26, axiom-(leq:plus), axiom-(list:cons), axiom-(less:plus:inverse)_013, axiom-(plus:times:distributive)_006, lemma-(a_reverse:types:2), axiom-(length:types), id40, axiom-(same_occ:termination), axiom-(not_same_occ:termination), axiom-(append:lh), axiom-(less:termination:2), id2, axiom-(append:member:1), axiom-(leq:one:failure), axiom-(occ:cons:diff), id11, axiom-(delete:member:1), id36, axiom-(leq:plus:second)_012, axiom-(leq:types), axiom-(less:plus:second), corollary-(rev:1), axiom-(append:uniqueness), axiom-(delete:types:2), axiom-(permutation:reflexive), axiom-(plus:zero), axiom-(less:plus)_008, id44, id22, id93, id6, id106, lemma-(rev:app), axiom-(list:termination), id55, axiom-(list:3), axiom-(app:lh:leq:first), axiom-(plus:less:less), lh/1, axiom-(occ:types)_017, axiom-(append:termination:2), axiom-(times:successor), axiom-(plus:types:1), id102, axiom-(delete:occ:diff), id33, lemma-(a_reverse:types:1), id47, axiom-(leq:termination:1), axiom-(list:2), id58, axiom-(plus:less:leq), id82, axiom-(lh:successor), axiom-(leq:one:success), axiom-(nat:ground), axiom-(length:uniqueness), axiom-(permutation:completeness), axiom-(length:ground), axiom-(permutation:member), id103, axiom-(less:transitive:successor), id78, axiom-(delete:app:1), theorem-(n_reverse:function), id1, (**)/2, axiom-(times:one)_005, id14, id89, id52, induction, axiom-(append:existence), axiom-(delete:ground), axiom-(plus:uniqueness), axiom-(app:member:1), axiom-(leq:less), lemma-(n_reverse:ground), id60, axiom-(occ:permutation), id28, axiom-(plus:ground:3), axiom-(less:leq:transitive), id18, id39, axiom-(less:different:zero), axiom-(permutation:length), axiom-(leq:transitive), axiom-(lh:zero), axiom-(lh:cons:first), axiom-(leq:reflexive), axiom-(member:ground), axiom-(less:plus), id72, axiom-(delete:member:existence), axiom-(leq:plus:first), id54, id99, lemma-(n_reverse:existence), axiom-(permutation:occ), axiom-(leq:totality), id12, axiom-(leq:antisymmetric), axiom-(times:leq:first), id35, theorem-(reverse:success), axiom-(occ:successor), id101, axiom-(plus:termination:1), axiom-(app:nil), axiom-(less:plus:first), axiom-(occ:uniqueness), corollary-(rev:nil), id57, axiom-(permutation:soundness), axiom-(delete:occ:eq), id83, axiom-(less:failure), axiom-(times:associative), axiom-(plus:termination:2), axiom-(occ:termination), axiom-(less:types), axiom-(less:strictness), id88, id46, id66, axiom-(occ:member:success)_019, lemma-(n_reverse:termination), id32, axiom-(append:member), axiom-(append:types:3), axiom-(less:axiom:successor), axiom-(app:lh:leq:second), axiom-(occ:zero), id29, occ/2, id104, id69, axiom-(leq:times:inverse), axiom-(less:termination:1), axiom-(times:less:second), axiom-(app:cons), axiom-(plus:times:distributive), axiom-(append:cons:different), axiom-(sub:cons:both), axiom-(leq:less:transitive), id77, axiom-(less:plus:second)_009, rev/1, id17, id7, axiom-(sub:member), axiom-(delete:termination:2), id107, axiom-(app:types:2), (@+)/2, axiom-(times:one), id8, axiom-(leq:plus)_007, axiom-(less:plus:inverse), axiom-(leq:plus:second), id15, axiom-(occ:nil), axiom-(app:associative), axiom-(plus:commutative), axiom-(delete:member:3), id23, id61, lemma-(a_reverse:n_reverse), axiom-(plus:leq:leq), axiom-(lh:cons:leq), axiom-(lh:cons), corollary-(rev:3), id87, axiom-(permutation:completeness)_018, axiom-(occ:ground), axiom-(permutation:app), id80, id4, axiom-(append:ground:1), axiom-(plus:injective:first), axiom-(occ:cons:eq), axiom-(append:equal:nil), axiom-(delete:nat_list), id65, axiom-(append:types:2), id53, axiom-(append:member:3), id76, axiom-(sub:nil), axiom-(less:one), id98, axiom-(occ:existence), id95, id31, id84, axiom-(sub:app:1), id100, id20, axiom-(times:successor)_004, axiom-(times:leq:second), axiom-(times:types), id73, axiom-(sub:transitive), axiom-(member:termination), axiom-(sub:cons), axiom-(append:lh:leq:first), axiom-(app:member:2), axiom-(plus:existence), lemma-(n_reverse:types), axiom-(occ:app), axiom-(permutation:symmetric), axiom-(permutation:types), axiom-(permutation:app:commutative), axiom-(occ:member:success), axiom-(list:1), axiom-(plus:ground:2), corollary-(rev:cons), axiom-(permutation:transitive), id3, axiom-(plus:termination:3), id68, axiom-(append:lh:leq:second), id27, axiom-(times:termination), axiom-(append:uniqueness:1), axiom-(length:existence), axiom-(plus:types), id38, axiom-(nat_list:list), id62, axiom-(permutation:termination), axiom-(nat:termination), axiom-(append:ground:2), axiom-(length:termination), axiom-(permutation:cons), lemma-(a_reverse:types:3), axiom-(plus:types:2), axiom-(member:occ:success), corollary-(rev:2), axiom-(append:termination:1), axiom-(append:types:4), axiom-(occ:member), axiom-(plus:associative), axiom-(plus:leq:less), axiom-(occ:types), axiom-(lh:nil), axiom-(member2:termination), axiom-(plus:successor), id108, id16, id50, id49, axiom-(app:ground:2), axiom-(member:append), axiom-(member:termination)_014, id79, axiom-(less:successor), axiom-(plus:types:3), axiom-(permutation:termination)_016, axiom-(permutation:ground), sub/2, id105, axiom-(delete:length), id90, axiom-(permutation:nat_list)
% 66.90/15.79 % No. of inferences in proof: 803
% 66.90/15.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15254 ms resp. 14431 ms w/o parsing
% 69.71/16.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.71/16.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------