%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT169_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 08:27:26 AM UTC 2026
% Result : Theorem 109.41s 29.94s
% Output : Refutation 110.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 112
% Syntax : Number of formulae : 579 ( 250 unt; 0 typ; 7 def)
% Number of atoms : 1342 ( 948 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 8381 ( 456 ~; 292 |; 123 &;7316 @)
% ( 32 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 11 con; 0-5 aty)
% Number of variables : 1515 ( 14 ^;1466 !; 28 ?;1515 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(butlast_decl,type,
butlast:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(distinct_decl,type,
distinct:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(dropWhile_decl,type,
dropWhile:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(hd_decl,type,
hd:
!>[TA: $tType] : ( ( TA @ list ) > TA ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(last_decl,type,
last:
!>[TA: $tType] : ( ( TA @ list ) > TA ) ).
thf(linorder_insort_key_decl,type,
linorder_insort_key:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > ( TB @ list ) > ( TB @ list ) ) ).
thf(linorder_sort_key_decl,type,
linorder_sort_key:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TB @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(maps_decl,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TA @ list @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(rev_decl,type,
rev:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(rotate1_decl,type,
rotate1:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(takeWhile_decl,type,
takeWhile:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: arrow_411405190le_alt ).
thf(b_decl,type,
b: arrow_411405190le_alt ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(sk2_decl,type,
sk2:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(sk3_decl,type,
sk3:
!>[TA: $tType] : ( ( TA @ list ) > TA ) ).
thf(sk4_decl,type,
sk4:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(sk5_decl,type,
sk5: arrow_411405190le_alt ).
thf(sk6_decl,type,
sk6: arrow_411405190le_alt ).
thf(sk7_decl,type,
sk7: arrow_411405190le_alt ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
@+[E: TA @ list] :
( ( ( B
= ( D @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( A @ ( TA @ append ) ) )
= C ) )
| ( ( ( B @ ( E @ ( TA @ append ) ) )
= D )
& ( A
= ( E @ ( C @ ( TA @ append ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [TA: $tType,A: TA @ list,B: TA @ list,C: TA,D: TA @ list] :
@+[E: TA @ list] :
( ( ( B @ ( E @ ( TA @ append ) ) )
= D )
& ( A
= ( E @ ( C @ ( TA @ cons ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [TA: $tType,A: TA @ list] :
@+[B: TA] :
? [C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [TA: $tType,A: TA @ list] :
@+[B: TA @ list] :
( A
= ( B @ ( A @ ( TA @ sk3 ) @ ( TA @ cons ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: arrow_411405190le_alt] :
? [B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: arrow_411405190le_alt] :
? [B: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( sk5 @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk5 @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ) ) ).
thf(56,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
<=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_distinct__length__2__or__more) ).
thf(384,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(18,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_self__append__conv2) ).
thf(184,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( B @ ( A @ ( TA @ append ) ) ) ) )
& ( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(185,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
| ( A
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ( B
!= ( B @ ( A @ ( TA @ append ) ) ) ) ) ),
inference(cnf,[status(esa)],[184]) ).
thf(187,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
| ( A
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[185]) ).
thf(189,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( B @ ( A @ ( TA @ append ) ) )
= B )
| ( A
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[187]) ).
thf(190,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
inference(simp,[status(thm)],[189]) ).
thf(40,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_append__is__Nil__conv) ).
thf(316,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(317,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) )
| ( B
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ( ( A @ ( B @ ( TA @ append ) ) )
!= ( TA @ nil ) ) )
& ( ( B
= ( TA @ nil ) )
| ( ( A @ ( B @ ( TA @ append ) ) )
!= ( TA @ nil ) ) ) ),
inference(cnf,[status(esa)],[316]) ).
thf(320,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) )
| ( B
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[317]) ).
thf(323,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) )
| ( B
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[323]) ).
thf(23,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Nil__is__rev__conv) ).
thf(203,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(204,plain,
! [TA: $tType,A: TA @ list] :
( ( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
| ( A
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ( ( TA @ nil )
!= ( A @ ( TA @ rev ) ) ) ) ),
inference(cnf,[status(esa)],[203]) ).
thf(206,plain,
! [TA: $tType,A: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
| ( A
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[204]) ).
thf(208,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[206]) ).
thf(209,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[208]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( B @ ( TA @ rev ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rev__append) ).
thf(136,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( B @ ( TA @ rev ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(137,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( B @ ( TA @ rev ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(138,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( B @ ( TA @ rev ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(705,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( A @ ( B @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,138]) ).
thf(706,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(723,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[706]) ).
thf(741,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[209,723]) ).
thf(742,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[741:[]]) ).
thf(765,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[742]) ).
thf(788,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[209,765]) ).
thf(789,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[788:[]]) ).
thf(814,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[789]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rev__rev__ident) ).
thf(124,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(125,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
inference(cnf,[status(esa)],[124]) ).
thf(126,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
inference(lifteq,[status(thm)],[125]) ).
thf(830,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( A @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[814,126]) ).
thf(831,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[830:[bind(A,$thf( TB @ nil ))]]) ).
thf(843,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[831]) ).
thf(854,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[324,843]) ).
thf(855,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[854:[]]) ).
thf(876,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[855]) ).
thf(743,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[209,723]) ).
thf(744,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[743:[]]) ).
thf(766,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[744]) ).
thf(972,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[876,766]) ).
thf(973,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[972:[]]) ).
thf(996,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[973]) ).
thf(850,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( B @ ( TB @ append ) ) @ ( TB @ rev ) ) )
| ( ( TB @ nil )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[843,138]) ).
thf(851,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(874,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[851]) ).
thf(1050,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[996,874]) ).
thf(1051,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[1050:[]]) ).
thf(1094,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[1051]) ).
thf(1155,plain,
! [TB: $tType,A: TB @ list] :
( ( ( A @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( A @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[190,1094]) ).
thf(1156,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[1155:[bind(A,$thf( TB @ nil ))]]) ).
thf(1176,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[1156]) ).
thf(1223,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
!= ( A @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
= A ) ),
inference(paramod_ordered,[status(thm)],[1176,190]) ).
thf(1224,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[1223:[bind(A,$thf( TB @ nil @ ( TB @ rev ) ))]]) ).
thf(1242,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1201,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
!= ( A @ ( B @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1176,138]) ).
thf(1202,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[1201:[bind(A,$thf( TB @ nil @ ( TB @ rev ) )),bind(B,$thf( TB @ nil ))]]) ).
thf(1246,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[1202]) ).
thf(5478,plain,
! [TB: $tType,A: TB @ list] :
( ( ( A @ ( TB @ rev ) @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( A @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[126,1246]) ).
thf(5479,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[5478:[bind(A,$thf( TB @ nil ))]]) ).
thf(5582,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[5479]) ).
thf(5689,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1242,5582]) ).
thf(5690,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[5689:[]]) ).
thf(5857,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[5690]) ).
thf(5424,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[1242,1246]) ).
thf(5425,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[5424:[]]) ).
thf(5564,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[5425]) ).
thf(27,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_self__append__conv) ).
thf(236,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(237,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( A
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ( B
!= ( A @ ( B @ ( TA @ append ) ) ) ) ) ),
inference(cnf,[status(esa)],[236]) ).
thf(239,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( A
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[237]) ).
thf(241,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
| ( A
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(242,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
inference(simp,[status(thm)],[241]) ).
thf(6533,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[5564,242]) ).
thf(6534,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[6533:[bind(A,$thf( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) ))]]) ).
thf(6608,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[6534]) ).
thf(6705,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[5857,6608]) ).
thf(6706,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[6705:[]]) ).
thf(6773,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[6706]) ).
thf(7474,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[6773,126]) ).
thf(7475,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[7474:[bind(A,$thf( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ))]]) ).
thf(7533,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[7475]) ).
thf(7427,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(rewrite,[status(thm)],[843,6773]) ).
thf(7544,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(rewrite,[status(thm)],[6773,7427]) ).
thf(7807,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) )
!= ( A @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[7533,126]) ).
thf(7808,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[7807:[bind(A,$thf( TB @ nil @ ( TB @ rev ) ))]]) ).
thf(7822,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[7808]) ).
thf(8172,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(rewrite,[status(thm)],[7544,7822]) ).
thf(8567,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(rewrite,[status(thm)],[7533,8172]) ).
thf(8565,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(rewrite,[status(thm)],[7822,8172]) ).
thf(8622,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( B @ ( TB @ append ) ) @ ( TB @ rev ) ) )
| ( ( TB @ nil )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8565,138]) ).
thf(8623,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[8622:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(8728,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[8623]) ).
thf(8834,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[8567,8728]) ).
thf(8835,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[8834:[]]) ).
thf(8960,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[8835]) ).
thf(68,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_List_Onull__def) ).
thf(442,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) )
& ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(443,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
| ( A
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ~ ( A @ ( TA @ null ) ) ) ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
| ~ ( A @ ( TA @ null ) ) ),
inference(cnfConj,[status(thm)],[443]) ).
thf(446,plain,
! [TA: $tType,A: TA @ list] :
( ~ ( A @ ( TA @ null ) )
| ( A
= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[444]) ).
thf(69,axiom,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_alt3) ).
thf(449,plain,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(450,plain,
arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk5 @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ),
inference(cnf,[status(esa)],[449]) ).
thf(1,conjecture,
? [A: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ? [A: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(107,plain,
~ ? [A: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(108,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(cnf,[status(esa)],[107]) ).
thf(637,plain,
! [A: arrow_411405190le_alt] :
( ( ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk5 @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
!= ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[450,108]) ).
thf(638,plain,
! [A: arrow_411405190le_alt] :
( ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk5 @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
!= ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ),
inference(simp,[status(thm)],[637]) ).
thf(639,plain,
! [A: arrow_411405190le_alt] :
( ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk5 @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) ) ),
inference(simp,[status(thm)],[638]) ).
thf(640,plain,
! [A: arrow_411405190le_alt] :
( ( ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) ) )
| ( sk5 != a ) ),
inference(simp,[status(thm)],[639]) ).
thf(1849,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( arrow_411405190le_alt @ nil )
!= ( arrow_411405190le_alt @ nil ) )
| ( ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) ) )
| ( sk5 != a )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,640]) ).
thf(1850,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) ) )
| ( sk5 != a )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(pattern_uni,[status(thm)],[1849:[]]) ).
thf(94,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) @ ( TA @ last ) )
= ( A @ ( TA @ hd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_last__rev) ).
thf(555,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) @ ( TA @ last ) )
= ( A @ ( TA @ hd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(39,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
= A )
<=> ( ( ( A @ ( TA @ last ) )
= B )
& ( ( A @ ( TA @ butlast ) )
= C )
& ( A
!= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_snoc__eq__iff__butlast) ).
thf(302,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( ( ( A @ ( TA @ last ) )
= B )
& ( ( A @ ( TA @ butlast ) )
= C )
& ( A
!= ( TA @ nil ) ) )
=> ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
= A ) )
& ( ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
= A )
=> ( ( ( A @ ( TA @ last ) )
= B )
& ( ( A @ ( TA @ butlast ) )
= C )
& ( A
!= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(303,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
= A )
| ( ( A @ ( TA @ last ) )
!= B )
| ( ( A @ ( TA @ butlast ) )
!= C )
| ( A
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ last ) )
= B )
| ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
!= A ) )
& ( ( ( A @ ( TA @ butlast ) )
= C )
| ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
!= A ) )
& ( ( A
!= ( TA @ nil ) )
| ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
!= A ) ) ),
inference(cnf,[status(esa)],[302]) ).
thf(304,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
| ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
!= A ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(308,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
| ( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ append ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[304]) ).
thf(309,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) )
!= ( TA @ nil ) ),
inference(simp,[status(thm)],[308]) ).
thf(663,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
!= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[324,309]) ).
thf(664,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) ),
inference(simp,[status(thm)],[663]) ).
thf(665,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( A @ ( TB @ cons ) ) )
!= ( TB @ nil ) )
| ( ( TB @ nil )
!= B ) ),
inference(simp,[status(thm)],[664]) ).
thf(666,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(simp,[status(thm)],[665]) ).
thf(47,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) @ ( TA @ hd ) )
= ( A @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_hd__rev) ).
thf(352,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) @ ( TA @ hd ) )
= ( A @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(50,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_null__rec_I1_J) ).
thf(364,plain,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(365,plain,
! [TA: $tType,B: TA,A: TA @ list] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
inference(cnf,[status(esa)],[364]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_sort__key__simps_I2_J) ).
thf(408,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(16,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_equal__list__def) ).
thf(174,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ list @ equal_equal ) ) ) )
& ( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(175,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
| ( B != A ) )
& ( ( B = A )
| ~ ( A @ ( B @ ( TA @ list @ equal_equal ) ) ) ) ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ list @ equal_equal ) ) ) ),
inference(cnfConj,[status(thm)],[175]) ).
thf(178,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ~ ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(9432,plain,
! [C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: arrow_411405190le_alt @ list] :
( ( B
!= ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) ) )
| ~ ( A @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,108]) ).
thf(9433,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9432:[bind(A,$thf( A )),bind(B,$thf( arrow_411405190le_alt @ nil @ ( D @ ( arrow_411405190le_alt @ cons ) ) )),bind(C,$thf( D ))]]) ).
thf(9791,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[9433]) ).
thf(25,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( C
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rev__eq__Cons__iff) ).
thf(213,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( C
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) )
=> ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( C
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(214,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C
!= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) )
& ( ( C
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) )
| ( ( C @ ( TA @ rev ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(215,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( C
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) )
| ( ( C @ ( TA @ rev ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[214]) ).
thf(217,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( C
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) )
| ( ( C @ ( TA @ rev ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(7655,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[7544,126]) ).
thf(7656,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[7655:[bind(A,$thf( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ))]]) ).
thf(7706,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[7656]) ).
thf(7622,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( B @ ( TB @ append ) ) @ ( TB @ rev ) ) )
| ( ( TB @ nil )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7544,138]) ).
thf(7623,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[7622:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(7695,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[7623]) ).
thf(7882,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[7706,7695]) ).
thf(7883,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[7882:[]]) ).
thf(8072,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[7883]) ).
thf(13355,plain,
! [TB: $tType,A: TB @ list] :
( ( ( A @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( A @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[190,8072]) ).
thf(13356,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[13355:[bind(A,$thf( TB @ nil ))]]) ).
thf(13484,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[13356]) ).
thf(13705,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
!= ( A @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
= A ) ),
inference(paramod_ordered,[status(thm)],[13484,190]) ).
thf(13706,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[13705:[bind(A,$thf( TB @ nil @ ( TB @ rev ) ))]]) ).
thf(13793,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[13706]) ).
thf(8187,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( B @ ( TB @ append ) ) @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7822,138]) ).
thf(8188,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[8187:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(8308,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[8188]) ).
thf(16157,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[13793,8308]) ).
thf(16158,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[16157:[]]) ).
thf(16284,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[16158]) ).
thf(16495,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13793,16284]) ).
thf(16496,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[16495:[]]) ).
thf(16628,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[16496]) ).
thf(16746,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( A @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[16628,126]) ).
thf(16747,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[16746:[bind(A,$thf( TB @ nil ))]]) ).
thf(16776,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[16747]) ).
thf(16962,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( A @ ( B @ ( TB @ append ) ) @ ( TB @ rev ) ) )
| ( ( TB @ nil )
= ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16776,138]) ).
thf(16963,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[16962:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(17142,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[16963]) ).
thf(18994,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
!= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[17142,309]) ).
thf(18995,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) ),
inference(simp,[status(thm)],[18994]) ).
thf(19001,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
!= B ) ),
inference(simp,[status(thm)],[18995]) ).
thf(19081,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( TA @ rev ) )
!= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(simp,[status(thm)],[19001]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rev__is__rev__conv) ).
thf(116,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) ) )
& ( ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(117,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) )
| ( B != A ) )
& ( ( B = A )
| ( ( B @ ( TA @ rev ) )
!= ( A @ ( TA @ rev ) ) ) ) ),
inference(cnf,[status(esa)],[116]) ).
thf(118,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( B = A )
| ( ( B @ ( TA @ rev ) )
!= ( A @ ( TA @ rev ) ) ) ),
inference(cnfConj,[status(thm)],[117]) ).
thf(120,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( B = A )
| ( ( B @ ( TA @ rev ) )
!= ( A @ ( TA @ rev ) ) ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_last__ConsR) ).
thf(200,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(201,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) )
| ( B
= ( TA @ nil ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(202,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) )
| ( B
= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(104,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rev__cases) ).
thf(597,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(63,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ append ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ butlast ) )
= ( A @ ( TA @ butlast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_butlast__append) ).
thf(417,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ append ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ butlast ) )
= ( A @ ( TA @ butlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_append__self__conv) ).
thf(288,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= B ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(38,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rotate1__is__Nil__conv) ).
thf(295,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(296,plain,
! [TA: $tType,A: TA @ list] :
( ( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ( ( A @ ( TA @ rotate1 ) )
!= ( TA @ nil ) ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(298,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(300,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[298]) ).
thf(301,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rotate1 ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[300]) ).
thf(1966,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( arrow_411405190le_alt @ nil )
!= ( arrow_411405190le_alt @ nil ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,108]) ).
thf(1967,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(pattern_uni,[status(thm)],[1966:[]]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insort__key_Osimps_I1_J) ).
thf(587,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(46,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: bool @ ( TA @ fun )] :
( ( ( C @ ( D @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ~ ( B @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C
= ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_dropWhile__eq__Cons__conv) ).
thf(344,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: bool @ ( TA @ fun )] :
( ( ( ~ ( B @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C
= ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ~ ( B @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C
= ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_list_Orecs_I2_J) ).
thf(194,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(195,plain,
! [TA: $tType,TB: $tType,D: TA,C: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TB,A: TB @ list] :
( ( A @ ( B @ ( TB @ cons ) ) @ ( C @ ( D @ ( TB @ ( TA @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TB @ ( TA @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[194]) ).
thf(196,plain,
! [TA: $tType,TB: $tType,D: TA,C: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TB,A: TB @ list] :
( ( A @ ( C @ ( D @ ( TB @ ( TA @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ cons ) ) @ ( C @ ( D @ ( TB @ ( TA @ list_rec ) ) ) ) ) ),
inference(lifteq,[status(thm)],[195]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_append__eq__append__conv2) ).
thf(146,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(147,plain,
! [TA: $tType,E: TA @ list,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( C
!= ( A @ ( E @ ( TA @ append ) ) ) )
| ( ( E @ ( D @ ( TA @ append ) ) )
!= B ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( E @ ( TA @ append ) ) )
!= A )
| ( D
!= ( E @ ( B @ ( TA @ append ) ) ) ) )
& ( ( C
= ( A @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) ) )
| ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( D @ ( TA @ append ) ) )
= B )
| ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( C
= ( A @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) ) )
| ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( D @ ( TA @ append ) ) )
= B )
| ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ) ),
inference(cnf,[status(esa)],[146]) ).
thf(151,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( C
= ( A @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) ) )
| ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(157,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( A @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= C )
| ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( B @ ( TA @ append ) ) )
= D )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(41,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( TA @ nil @ ( A @ ( TA @ last ) @ ( TA @ cons ) ) @ ( A @ ( TA @ butlast ) @ ( TA @ append ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_append__butlast__last__id) ).
thf(325,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( TA @ nil @ ( A @ ( TA @ last ) @ ( TA @ cons ) ) @ ( A @ ( TA @ butlast ) @ ( TA @ append ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(445,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
| ( A
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[443]) ).
thf(447,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
| ( A
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[445]) ).
thf(448,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(simp,[status(thm)],[447]) ).
thf(12,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_append__assoc) ).
thf(162,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(163,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(164,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
inference(lifteq,[status(thm)],[163]) ).
thf(53,axiom,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_distinct__singleton) ).
thf(376,plain,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(377,plain,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
inference(cnf,[status(esa)],[376]) ).
thf(9434,plain,
! [C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: arrow_411405190le_alt @ list] :
( ( B
!= ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) ) )
| ~ ( A @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,108]) ).
thf(9435,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9434:[bind(A,$thf( A )),bind(B,$thf( arrow_411405190le_alt @ nil @ ( F @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) )),bind(C,$thf( F ))]]) ).
thf(9792,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[9435]) ).
thf(17180,plain,
! [TA: $tType,C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: TA] :
( ( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) )
!= ( B @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ $true
| ~ ( B @ ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[377,9792]) ).
thf(17181,plain,
! [TA: $tType,C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: TA] :
( ( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) )
!= ( B @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ ( B @ ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[17180]) ).
thf(17182,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(pattern_uni,[status(thm)],[17181:[bind(A,$thf( a )),bind(B,$thf( arrow_411405190le_alt @ nil )),bind_type(TA,$thf( arrow_411405190le_alt ))]]) ).
thf(17232,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[17182]) ).
thf(17265,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( arrow_411405190le_alt @ nil )
!= ( arrow_411405190le_alt @ nil ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,17232]) ).
thf(17266,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(pattern_uni,[status(thm)],[17265:[]]) ).
thf(1064,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
!= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[874,309]) ).
thf(1065,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) ),
inference(simp,[status(thm)],[1064]) ).
thf(1074,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
!= B ) ),
inference(simp,[status(thm)],[1065]) ).
thf(1088,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( TA @ rev ) )
!= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(simp,[status(thm)],[1074]) ).
thf(1101,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( ( A @ ( TB @ rev ) @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( A
!= ( TB @ nil @ ( B @ ( TB @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[126,1088]) ).
thf(1104,plain,
! [TB: $tType,A: TB] :
( ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1106,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) @ ( TA @ rev ) )
!= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[1104]) ).
thf(6727,plain,
! [TB: $tType,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ rev ) )
!= ( A @ ( TB @ rev ) @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[6608,126]) ).
thf(6728,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[6727:[bind(A,$thf( TB @ nil ))]]) ).
thf(6752,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[6728]) ).
thf(6777,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) @ ( TA @ rev ) )
!= ( TA @ nil ) ),
inference(rewrite,[status(thm)],[1106,6752]) ).
thf(8136,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ rev ) ) )
| ( ( TB @ nil )
!= ( TB @ nil ) )
| ~ ( A @ ( TB @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,6777]) ).
thf(8137,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ rev ) ) )
| ~ ( A @ ( TB @ null ) ) ),
inference(simp,[status(thm)],[8136]) ).
thf(8138,plain,
! [TB: $tType,A: TB] :
~ ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ rev ) @ ( TB @ null ) ),
inference(pattern_uni,[status(thm)],[8137:[bind(A,$thf( TB @ nil @ ( E @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ rev ) )),bind(B,$thf( E ))]]) ).
thf(8158,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) @ ( TA @ rev ) @ ( TA @ null ) ),
inference(simp,[status(thm)],[8138]) ).
thf(8897,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
!= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[8728,309]) ).
thf(8898,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( B @ ( TB @ append ) ) ) ),
inference(simp,[status(thm)],[8897]) ).
thf(8914,plain,
! [TB: $tType,B: TB @ list,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( A @ ( TB @ cons ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) )
!= B ) ),
inference(simp,[status(thm)],[8898]) ).
thf(8992,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( TA @ rev ) )
!= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(simp,[status(thm)],[8914]) ).
thf(10520,plain,
! [TB: $tType,C: TB,B: TB @ list,A: TB @ list] :
( ( B
!= ( TB @ nil @ ( C @ ( TB @ cons ) ) ) )
| ( A
!= ( TB @ nil @ ( TB @ rev ) ) )
| ~ ( A @ ( B @ ( TB @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,8992]) ).
thf(10521,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( TB @ rev ) ) )
| ~ ( A @ ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[10520:[bind(A,$thf( A )),bind(B,$thf( TB @ nil @ ( D @ ( TB @ cons ) ) )),bind(C,$thf( D ))]]) ).
thf(10551,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[10521]) ).
thf(58,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_append__Nil2) ).
thf(396,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list_Orecs_I1_J) ).
thf(411,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(177,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[175]) ).
thf(179,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(180,plain,
! [TA: $tType,A: TA @ list] : ( A @ ( A @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(17281,plain,
! [C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: arrow_411405190le_alt @ list] :
( ( A
!= ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,17232]) ).
thf(17282,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[17281:[bind(A,$thf( arrow_411405190le_alt @ nil @ ( F @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(17284,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[17282]) ).
thf(23849,plain,
! [TA: $tType,C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: TA @ list] :
( ( ( A @ ( A @ ( TA @ list @ equal_equal ) ) )
!= ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) )
| ~ $true
| ~ ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[180,17284]) ).
thf(23850,plain,
! [TA: $tType,C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: TA @ list] :
( ( ( A @ ( A @ ( TA @ list @ equal_equal ) ) )
!= ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[23849]) ).
thf(23851,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(pattern_uni,[status(thm)],[23850:[bind(A,$thf( arrow_411405190le_alt @ nil )),bind(B,$thf( arrow_411405190le_alt @ nil )),bind_type(TA,$thf( arrow_411405190le_alt ))]]) ).
thf(23909,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[23851]) ).
thf(84,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list_Osimps_I2_J) ).
thf(505,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(506,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(cnf,[status(esa)],[505]) ).
thf(507,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(lifteq,[status(thm)],[506]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_not__Cons__self) ).
thf(243,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_butlast_Osimps_I1_J) ).
thf(378,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(379,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
inference(cnf,[status(esa)],[378]) ).
thf(380,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
inference(lifteq,[status(thm)],[379]) ).
thf(67,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ distinct ) )
=> ( A @ ( TA @ butlast ) @ ( TA @ distinct ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_distinct__butlast) ).
thf(439,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ distinct ) )
=> ( A @ ( TA @ butlast ) @ ( TA @ distinct ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8832,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[8567,8728]) ).
thf(8833,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[8832:[]]) ).
thf(8959,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[8833]) ).
thf(55,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_last__appendR) ).
thf(381,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(26,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_append__eq__Cons__conv) ).
thf(220,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
& ( D
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ append ) ) ) )
& ( ( TB @ nil @ ( TB @ rotate1 ) )
= ( TB @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rotate__simps) ).
thf(366,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ append ) ) ) )
& ( ( TB @ nil @ ( TB @ rotate1 ) )
= ( TB @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ cons ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_butlast_Osimps_I2_J) ).
thf(424,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ cons ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(425,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ cons ) ) ) )
| ( B
= ( TA @ nil ) ) )
& ( ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) )
| ( B
!= ( TA @ nil ) ) ) ),
inference(cnf,[status(esa)],[424]) ).
thf(426,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) )
| ( B
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[425]) ).
thf(428,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) )
| ( B
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[426]) ).
thf(429,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[428]) ).
thf(34,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_not__Cons__self2) ).
thf(275,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(165,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(74,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_splice_Osimps_I2_J) ).
thf(467,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(221,plain,
! [TA: $tType,E: TA @ list,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( ( C @ ( E @ ( TA @ append ) ) )
!= A )
| ( D
!= ( E @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C
!= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( D
!= ( TA @ nil ) ) )
& ( ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( B @ ( TA @ cons ) ) ) )
| ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( D
= ( TA @ nil ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( B @ ( TA @ cons ) ) ) )
| ( D
= ( TA @ nil ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(cnf,[status(esa)],[220]) ).
thf(224,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C
!= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( D
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(228,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C
!= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( D
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(229,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_last__ConsL) ).
thf(252,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_splice__Nil2) ).
thf(197,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(66,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_equal__Nil__null) ).
thf(435,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) ) )
& ( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(9430,plain,
! [C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: arrow_411405190le_alt @ list] :
( ( B
!= ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) ) )
| ~ ( A @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,108]) ).
thf(9431,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9430:[bind(A,$thf( A )),bind(B,$thf( arrow_411405190le_alt @ nil @ ( H @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) )),bind(C,$thf( H ))]]) ).
thf(9790,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[9431]) ).
thf(100,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) @ ( TA @ distinct ) )
<=> ( A @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_distinct1__rotate) ).
thf(583,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ distinct ) )
=> ( A @ ( TA @ rotate1 ) @ ( TA @ distinct ) ) )
& ( ( A @ ( TA @ rotate1 ) @ ( TA @ distinct ) )
=> ( A @ ( TA @ distinct ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(81,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( C @ ( TA @ dropWhile ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dropWhile_Osimps_I2_J) ).
thf(493,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( C @ ( TA @ dropWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(92,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_takeWhile_Osimps_I1_J) ).
thf(549,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(550,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
inference(cnf,[status(esa)],[549]) ).
thf(551,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
inference(lifteq,[status(thm)],[550]) ).
thf(1105,plain,
! [TB: $tType,A: TB] :
( ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( TB @ rev ) )
!= ( TB @ nil ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1107,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) )
!= ( TA @ nil ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1826,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ rev ) ) )
| ( ( TB @ nil )
!= ( TB @ nil ) )
| ~ ( A @ ( TB @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,1107]) ).
thf(1827,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ rev ) ) )
| ~ ( A @ ( TB @ null ) ) ),
inference(simp,[status(thm)],[1826]) ).
thf(1828,plain,
! [TB: $tType,A: TB] :
~ ( TB @ nil @ ( A @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ null ) ),
inference(pattern_uni,[status(thm)],[1827:[bind(A,$thf( TB @ nil @ ( D @ ( TB @ cons ) ) @ ( TB @ rev ) )),bind(B,$thf( D ))]]) ).
thf(2112,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) @ ( TA @ null ) ),
inference(simp,[status(thm)],[1828]) ).
thf(36,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA,D: bool @ ( TA @ fun )] :
( ~ ( C @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( D @ ( TA @ takeWhile ) ) )
= ( B @ ( D @ ( TA @ takeWhile ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_takeWhile__tail) ).
thf(285,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA,D: bool @ ( TA @ fun )] :
( ~ ( C @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( D @ ( TA @ takeWhile ) ) )
= ( B @ ( D @ ( TA @ takeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(87,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Cons__eq__append__conv) ).
thf(519,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(150,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( D @ ( TA @ append ) ) )
= B )
| ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(156,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( D @ ( TA @ append ) ) )
= B )
| ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(13221,plain,
! [TB: $tType,C: TB @ list,B: TB @ list,A: TB @ list] :
( ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
!= ( A @ ( B @ ( C @ ( TB @ append ) ) @ ( TB @ append ) ) ) )
| ( ( TB @ nil )
= ( A @ ( B @ ( TB @ append ) ) @ ( C @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8072,164]) ).
thf(13222,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[13221:[bind(A,$thf( TB @ nil @ ( TB @ rev ) )),bind(B,$thf( TB @ nil )),bind(C,$thf( TB @ nil ))]]) ).
thf(13576,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[13222]) ).
thf(17263,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( arrow_411405190le_alt @ nil )
!= ( arrow_411405190le_alt @ nil ) )
| ~ ( arrow_411405190le_alt @ nil @ ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,17232]) ).
thf(17264,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( arrow_411405190le_alt @ nil @ ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(pattern_uni,[status(thm)],[17263:[]]) ).
thf(186,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( A
= ( TA @ nil ) )
| ( B
!= ( B @ ( A @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[185]) ).
thf(188,plain,
! [TA: $tType,B: TA @ list,A: TA @ list] :
( ( A
= ( TA @ nil ) )
| ( ( B @ ( A @ ( TA @ append ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(82,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_splice_Osimps_I1_J) ).
thf(499,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TB @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TB @ ( TA @ linorder_sort_key ) ) ) )
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_sort__key__simps_I1_J) ).
thf(537,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TB @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TB @ ( TA @ linorder_sort_key ) ) ) )
= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(77,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_distinct_Osimps_I1_J) ).
thf(476,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(80,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Cons__eq__appendI) ).
thf(489,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(102,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_eq__Nil__appendI) ).
thf(590,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(91,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list__ex1__simps_I1_J) ).
thf(547,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( TA @ butlast ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_butlast__snoc) ).
thf(210,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( TA @ butlast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(211,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( TA @ butlast ) )
= B ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( TA @ butlast ) )
= B ),
inference(lifteq,[status(thm)],[211]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_neq__Nil__conv) ).
thf(256,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_same__append__eq) ).
thf(109,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_last_Osimps) ).
thf(328,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons ) ) @ ( TA @ last ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ maps ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_maps__simps_I2_J) ).
thf(393,plain,
! [TA: $tType,TB: $tType,A: TA @ list @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ maps ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(86,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ list @ fun )] :
( ( TA @ nil @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rev__induct) ).
thf(515,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ list @ fun )] :
( ( TA @ nil @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ dropWhile ) ) @ ( A @ ( B @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_takeWhile__dropWhile__id) ).
thf(171,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ dropWhile ) ) @ ( A @ ( B @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(172,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: TA @ list] :
( ( A @ ( B @ ( TA @ dropWhile ) ) @ ( A @ ( B @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) )
= A ),
inference(cnf,[status(esa)],[171]) ).
thf(173,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: TA @ list] :
( ( A @ ( B @ ( TA @ dropWhile ) ) @ ( A @ ( B @ ( TA @ takeWhile ) ) @ ( TA @ append ) ) )
= A ),
inference(lifteq,[status(thm)],[172]) ).
thf(97,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Oexhaust) ).
thf(569,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B @ ( TA @ rev ) )
= A )
<=> ( B
= ( A @ ( TA @ rev ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rev__swap) ).
thf(128,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( A @ ( TA @ rev ) ) )
=> ( ( B @ ( TA @ rev ) )
= A ) )
& ( ( ( B @ ( TA @ rev ) )
= A )
=> ( B
= ( A @ ( TA @ rev ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(85,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_rev__is__Nil__conv) ).
thf(508,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(9225,plain,
! [TB: $tType,C: TB,B: TB @ list,A: TB @ list] :
( ( B
!= ( TB @ nil @ ( C @ ( TB @ cons ) ) ) )
| ( A
!= ( TB @ nil ) )
| ~ ( A @ ( B @ ( TB @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,666]) ).
thf(9226,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil ) )
| ~ ( A @ ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9225:[bind(A,$thf( A )),bind(B,$thf( TB @ nil @ ( D @ ( TB @ cons ) ) )),bind(C,$thf( D ))]]) ).
thf(9689,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[9226]) ).
thf(95,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ dropWhile ) ) @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_distinct__dropWhile) ).
thf(558,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ dropWhile ) ) @ ( TA @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(10927,plain,
! [TA: $tType,C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: TA] :
( ( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) )
!= ( B @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ $true
| ~ ( B @ ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[377,9790]) ).
thf(10928,plain,
! [TA: $tType,C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: TA] :
( ( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) )
!= ( B @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ ( B @ ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[10927]) ).
thf(10929,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(pattern_uni,[status(thm)],[10928:[bind(A,$thf( D )),bind(B,$thf( arrow_411405190le_alt @ nil @ ( D @ ( arrow_411405190le_alt @ cons ) ) )),bind(C,$thf( C )),bind_type(TA,$thf( arrow_411405190le_alt ))]]) ).
thf(10971,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[10929]) ).
thf(166,plain,
~ ( fFalse @ pp ),
inference(polarity_switch,[status(thm)],[165]) ).
thf(149,plain,
! [TA: $tType,E: TA @ list,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( C
!= ( A @ ( E @ ( TA @ append ) ) ) )
| ( ( E @ ( D @ ( TA @ append ) ) )
!= B ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(160,plain,
! [TA: $tType,E: TA @ list,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( C
!= ( A @ ( E @ ( TA @ append ) ) ) )
| ( ( E @ ( D @ ( TA @ append ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(161,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( A @ ( C @ ( B @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) @ ( B @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(20110,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[324,8959]) ).
thf(20111,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[20110:[]]) ).
thf(20447,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[20111]) ).
thf(19,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_append__Nil) ).
thf(191,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(99,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_last__appendL) ).
thf(579,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(98,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= A )
<=> ( B
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_append__self__conv2) ).
thf(572,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= A ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= A )
=> ( B
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list_Osimps_I4_J) ).
thf(335,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TA,D: TB @ ( TA @ fun )] :
( ( ( C @ ( D @ ( TB @ ( TA @ aa ) ) ) )
!= ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insort__key__left__comm) ).
thf(181,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TA,D: TB @ ( TA @ fun )] :
( ( ( C @ ( D @ ( TB @ ( TA @ aa ) ) ) )
!= ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B @ ( TA @ rev ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) )
<=> ( B
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_rev__singleton__conv) ).
thf(540,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) )
=> ( ( B @ ( TA @ rev ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) )
& ( ( ( B @ ( TA @ rev ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) )
=> ( B
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(148,plain,
! [TA: $tType,E: TA @ list,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( E @ ( TA @ append ) ) )
!= A )
| ( D
!= ( E @ ( B @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(158,plain,
! [TA: $tType,E: TA @ list,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( E @ ( TA @ append ) ) )
!= A )
| ( D
!= ( E @ ( B @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(159,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( B @ ( C @ ( A @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( B @ ( C @ ( TA @ append ) ) @ ( A @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(110,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
| ( B != A ) )
& ( ( B = A )
| ( ( B @ ( C @ ( TA @ append ) ) )
!= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( B = A )
| ( ( B @ ( C @ ( TA @ append ) ) )
!= ( A @ ( C @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[110]) ).
thf(113,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( B = A )
| ( ( B @ ( C @ ( TA @ append ) ) )
!= ( A @ ( C @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(216,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C
!= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[214]) ).
thf(218,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C
!= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(219,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(simp,[status(thm)],[218]) ).
thf(225,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( D
= ( TA @ nil ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(230,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( D
= ( TA @ nil ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(244,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(cnf,[status(esa)],[243]) ).
thf(245,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( B @ ( A @ ( TA @ cons ) ) )
!= B ),
inference(lifteq,[status(thm)],[244]) ).
thf(9428,plain,
! [C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: arrow_411405190le_alt @ list] :
( ( B
!= ( arrow_411405190le_alt @ nil ) )
| ~ ( A @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,108]) ).
thf(9429,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9428:[bind(A,$thf( A )),bind(B,$thf( arrow_411405190le_alt @ nil ))]]) ).
thf(9789,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( A @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[9429]) ).
thf(49,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ takeWhile ) ) @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_distinct__takeWhile) ).
thf(362,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ takeWhile ) ) @ ( TA @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(70,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ hd ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_hd_Osimps) ).
thf(451,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ hd ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(477,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
inference(cnf,[status(esa)],[476]) ).
thf(93,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_list_Osimps_I3_J) ).
thf(552,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(88,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_distinct__insert) ).
thf(535,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dropWhile_Osimps_I1_J) ).
thf(607,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(608,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
inference(cnf,[status(esa)],[607]) ).
thf(609,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
inference(lifteq,[status(thm)],[608]) ).
thf(9229,plain,
! [TB: $tType,C: TB,B: TB @ list,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( C @ ( TB @ cons ) ) ) )
| ( B
!= ( TB @ nil ) )
| ~ ( A @ ( B @ ( TB @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,666]) ).
thf(9230,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil ) )
| ~ ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( A @ ( TB @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9229:[bind(A,$thf( TB @ nil @ ( D @ ( TB @ cons ) ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(9691,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ nil @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[9230]) ).
thf(103,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(594,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(72,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_null__rec_I2_J) ).
thf(462,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(641,plain,
! [A: arrow_411405190le_alt] :
( ( ( arrow_411405190le_alt @ nil @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) ) )
| ( sk6 != b )
| ( sk5 != a ) ),
inference(simp,[status(thm)],[640]) ).
thf(667,plain,
! [A: arrow_411405190le_alt] :
( ( ( arrow_411405190le_alt @ nil )
!= ( arrow_411405190le_alt @ nil ) )
| ( sk7 != A )
| ( sk6 != b )
| ( sk5 != a ) ),
inference(simp,[status(thm)],[641]) ).
thf(668,plain,
( ( sk6 != b )
| ( sk5 != a ) ),
inference(simp,[status(thm)],[667]) ).
thf(152,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( D @ ( TA @ append ) ) )
= B )
| ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( B @ ( TA @ append ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(155,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( D @ ( TA @ append ) ) )
= B )
| ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( B @ ( TA @ append ) ) )
= D )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(59,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Nil__is__append__conv) ).
thf(399,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( TA @ distinct ) )
<=> ( A @ ( TA @ distinct ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_distinct__sort) ).
thf(431,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A @ ( TA @ distinct ) )
=> ( A @ ( B @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( TA @ distinct ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( TA @ distinct ) )
=> ( A @ ( TA @ distinct ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_append__eq__appendI) ).
thf(167,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1146,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[996,1094]) ).
thf(1147,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[1146:[]]) ).
thf(1193,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[1147]) ).
thf(3908,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[324,1193]) ).
thf(3909,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[3908:[]]) ).
thf(4084,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[3909]) ).
thf(35,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( TA @ nil @ ( B @ ( TA @ cons ) ) )
= ( A @ ( TA @ rev ) ) )
<=> ( A
= ( TA @ nil @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_singleton__rev__conv) ).
thf(278,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( A
= ( TA @ nil @ ( B @ ( TA @ cons ) ) ) )
=> ( ( TA @ nil @ ( B @ ( TA @ cons ) ) )
= ( A @ ( TA @ rev ) ) ) )
& ( ( ( TA @ nil @ ( B @ ( TA @ cons ) ) )
= ( A @ ( TA @ rev ) ) )
=> ( A
= ( TA @ nil @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(10516,plain,
! [TB: $tType,C: TB,B: TB @ list,A: TB @ list] :
( ( B
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( A
!= ( TB @ nil @ ( C @ ( TB @ cons ) ) ) )
| ~ ( A @ ( B @ ( TB @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,8992]) ).
thf(10517,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( B @ ( TB @ cons ) ) ) )
| ~ ( A @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[10516:[bind(A,$thf( A )),bind(B,$thf( TB @ nil @ ( TB @ rev ) )),bind(C,$thf( C ))]]) ).
thf(10549,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[10517]) ).
thf(76,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_insert__Nil) ).
thf(473,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(548,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(cnf,[status(esa)],[547]) ).
thf(5,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(123,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_last__append) ).
thf(355,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(8189,plain,
! [TB: $tType,B: TB @ list,A: TB @ list] :
( ( ( A @ ( B @ ( TB @ append ) ) @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ rev ) ) )
| ( ( B @ ( TB @ rev ) @ ( A @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ) ),
inference(paramod_ordered,[status(thm)],[138,7822]) ).
thf(8190,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ rev ) @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil @ ( TB @ rev ) ) ),
inference(pattern_uni,[status(thm)],[8189:[bind(A,$thf( TB @ nil )),bind(B,$thf( TB @ nil ))]]) ).
thf(8311,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil @ ( TA @ rev ) ) ),
inference(simp,[status(thm)],[8190]) ).
thf(19167,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(rewrite,[status(thm)],[17142,8311]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
!= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insort__not__Nil) ).
thf(414,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
!= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9382,plain,
! [TB: $tType,C: TB,B: TB @ list,A: TB @ list] :
( ( A
!= ( TB @ nil @ ( C @ ( TB @ cons ) ) @ ( TB @ rev ) ) )
| ( B
!= ( TB @ nil ) )
| ~ ( A @ ( B @ ( TB @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,1107]) ).
thf(9383,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil ) )
| ~ ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( A @ ( TB @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9382:[bind(A,$thf( TB @ nil @ ( E @ ( TB @ cons ) ) @ ( TB @ rev ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(9766,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) @ ( TA @ nil @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[9383]) ).
thf(32,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list_Oinject) ).
thf(263,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(198,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(cnf,[status(esa)],[197]) ).
thf(199,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(lifteq,[status(thm)],[198]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_splice_Osimps_I3_J) ).
thf(502,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(7,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(127,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list_Osimps_I5_J) ).
thf(338,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_append__Cons) ).
thf(470,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(17279,plain,
! [C: arrow_411405190le_alt,B: arrow_411405190le_alt @ list,A: arrow_411405190le_alt @ list] :
( ( A
!= ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( B @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( A @ ( B @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,17232]) ).
thf(17280,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( arrow_411405190le_alt @ nil @ ( A @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[17279:[bind(A,$thf( arrow_411405190le_alt @ nil @ ( D @ ( arrow_411405190le_alt @ cons ) ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(17283,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ~ ( arrow_411405190le_alt @ nil @ ( A @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) )
| ~ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[17280]) ).
thf(10930,plain,
! [TA: $tType,B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( TA @ nil @ ( TA @ distinct ) )
!= ( A @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ $true
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,9790]) ).
thf(10931,plain,
! [TA: $tType,B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( TA @ nil @ ( TA @ distinct ) )
!= ( A @ ( arrow_411405190le_alt @ distinct ) ) )
| ~ ( A @ ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ) ),
inference(simp,[status(thm)],[10930]) ).
thf(10932,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(pattern_uni,[status(thm)],[10931:[bind(A,$thf( arrow_411405190le_alt @ nil )),bind_type(TA,$thf( arrow_411405190le_alt ))]]) ).
thf(10973,plain,
! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[10932]) ).
thf(153,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( C
= ( A @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) ) )
| ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(154,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( A @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= C )
| ( ( C @ ( A @ ( B @ ( C @ ( D @ ( TA @ sk1 ) ) ) ) @ ( TA @ append ) ) )
= A )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(105,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_eq__Nil__null) ).
thf(600,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(610,plain,
( ( ( fTrue @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,166]) ).
thf(611,plain,
( ( fTrue @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[610]) ).
thf(612,plain,
fTrue != fFalse,
inference(simp,[status(thm)],[611]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_append__same__eq) ).
thf(139,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(140,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
| ( C != A ) )
& ( ( C = A )
| ( ( B @ ( C @ ( TA @ append ) ) )
!= ( B @ ( A @ ( TA @ append ) ) ) ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( C = A )
| ( ( B @ ( C @ ( TA @ append ) ) )
!= ( B @ ( A @ ( TA @ append ) ) ) ) ),
inference(cnfConj,[status(thm)],[140]) ).
thf(143,plain,
! [TA: $tType,C: TA @ list,B: TA @ list,A: TA @ list] :
( ( C = A )
| ( ( B @ ( C @ ( TA @ append ) ) )
!= ( B @ ( A @ ( TA @ append ) ) ) ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(223,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( B @ ( TA @ cons ) ) ) )
| ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(231,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( B @ ( TA @ cons ) ) )
= D )
| ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(1099,plain,
! [TB: $tType,A: TB] :
( ( ( TB @ nil @ ( TB @ rev ) )
!= ( TB @ nil @ ( TB @ rev ) ) )
| ( ( TB @ nil @ ( A @ ( TB @ cons ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[996,1088]) ).
thf(1100,plain,
! [TB: $tType,A: TB] :
( ( TB @ nil @ ( A @ ( TB @ cons ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) ),
inference(pattern_uni,[status(thm)],[1099:[]]) ).
thf(1108,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) )
!= ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) ) ),
inference(simp,[status(thm)],[1100]) ).
thf(79,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ hd ) )
= ( B @ ( TA @ hd ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ hd ) )
= ( A @ ( TA @ hd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_hd__append) ).
thf(482,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ hd ) )
= ( B @ ( TA @ hd ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ hd ) )
= ( A @ ( TA @ hd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(21060,plain,
! [TB: $tType,A: TB @ list] :
( ( ( A @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( A @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[190,8960]) ).
thf(21061,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ rev ) @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[21060:[bind(A,$thf( TB @ nil ))]]) ).
thf(21208,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ rev ) @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[21061]) ).
thf(29,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ takeWhile ) ) )
= ( A @ ( C @ ( TA @ takeWhile ) ) @ ( B @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_takeWhile_Osimps_I2_J) ).
thf(246,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ takeWhile ) ) )
= ( A @ ( C @ ( TA @ takeWhile ) ) @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(78,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ distinct ) )
<=> ( A @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_distinct__rev) ).
thf(478,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ distinct ) )
=> ( A @ ( TA @ rev ) @ ( TA @ distinct ) ) )
& ( ( A @ ( TA @ rev ) @ ( TA @ distinct ) )
=> ( A @ ( TA @ distinct ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( TA @ last ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_last__snoc) ).
thf(272,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) @ ( TA @ last ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(205,plain,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
| ( ( TA @ nil )
!= ( A @ ( TA @ rev ) ) ) ),
inference(cnfConj,[status(thm)],[204]) ).
thf(207,plain,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
| ( ( A @ ( TA @ rev ) )
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(257,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( ( A
!= ( TA @ nil ) )
| ( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A
= ( A @ ( TA @ sk4 ) @ ( A @ ( TA @ sk3 ) @ ( TA @ cons ) ) ) )
| ( A
= ( TA @ nil ) ) ) ),
inference(cnf,[status(esa)],[256]) ).
thf(259,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
| ( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[257]) ).
thf(261,plain,
! [TA: $tType,C: TA @ list,B: TA,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
| ( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(262,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( B @ ( A @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(simp,[status(thm)],[261]) ).
thf(182,plain,
! [TA: $tType,TB: $tType,D: TA @ ( TB @ fun ),C: TB,B: TB,A: TB @ list] :
( ( ( A @ ( C @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) @ ( B @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) ) )
| ( ( C @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= ( B @ ( D @ ( TA @ ( TB @ aa ) ) ) ) )
| ~ ( TA @ linorder ) ),
inference(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [TA: $tType,TB: $tType,D: TA @ ( TB @ fun ),C: TB,B: TB,A: TB @ list] :
( ~ ( TA @ linorder )
| ( ( A @ ( C @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) @ ( B @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ linorder_insort_key ) ) ) ) ) )
| ( ( C @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= ( B @ ( D @ ( TA @ ( TB @ aa ) ) ) ) ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ maps ) ) ) @ ( B @ ( C @ ( TB @ list @ ( TA @ aa ) ) ) @ ( TB @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_maps__simps_I1_J) ).
thf(373,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ maps ) ) ) @ ( B @ ( C @ ( TB @ list @ ( TA @ aa ) ) ) @ ( TB @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(45,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rev_Osimps_I2_J) ).
thf(341,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( B @ ( TA @ cons ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(3906,plain,
! [TB: $tType] :
( ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) )
!= ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) ) )
| ( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[324,1193]) ).
thf(3907,plain,
! [TB: $tType] :
( ( TB @ nil @ ( TB @ nil @ ( TB @ append ) ) @ ( TB @ nil @ ( TB @ append ) ) )
= ( TB @ nil ) ),
inference(pattern_uni,[status(thm)],[3906:[]]) ).
thf(4083,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ nil @ ( TA @ append ) ) @ ( TA @ nil @ ( TA @ append ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[3907]) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: TB @ list @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TB @ ( TA @ maps ) ) ) )
= ( TB @ nil ) ),
inference(cnf,[status(esa)],[393]) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: TB @ list @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TB @ ( TA @ maps ) ) ) )
= ( TB @ nil ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rev_Osimps_I1_J) ).
thf(464,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(9376,plain,
! [TB: $tType,C: TB,B: TB @ list,A: TB @ list] :
( ( B
!= ( TB @ nil @ ( C @ ( TB @ cons ) ) @ ( TB @ rev ) ) )
| ( A
!= ( TB @ nil ) )
| ~ ( A @ ( B @ ( TB @ list @ equal_equal ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,1107]) ).
thf(9377,plain,
! [TB: $tType,B: TB,A: TB @ list] :
( ( A
!= ( TB @ nil ) )
| ~ ( A @ ( TB @ nil @ ( B @ ( TB @ cons ) ) @ ( TB @ rev ) @ ( TB @ list @ equal_equal ) ) ) ),
inference(pattern_uni,[status(thm)],[9376:[bind(A,$thf( A )),bind(B,$thf( TB @ nil @ ( E @ ( TB @ cons ) ) @ ( TB @ rev ) )),bind(C,$thf( E ))]]) ).
thf(9763,plain,
! [TA: $tType,A: TA] :
~ ( TA @ nil @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ rev ) @ ( TA @ list @ equal_equal ) ) ),
inference(simp,[status(thm)],[9377]) ).
thf(595,plain,
a != b,
inference(polarity_switch,[status(thm)],[594]) ).
thf(596,plain,
b != a,
inference(lifteq,[status(thm)],[595]) ).
thf(276,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(cnf,[status(esa)],[275]) ).
thf(277,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(lifteq,[status(thm)],[276]) ).
thf(1847,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( arrow_411405190le_alt @ nil )
!= ( arrow_411405190le_alt @ nil ) )
| ( ( A @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) ) )
| ( sk5 != a )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(paramod_ordered,[status(thm)],[446,640]) ).
thf(1848,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt @ list] :
( ( ( A @ ( sk7 @ ( arrow_411405190le_alt @ cons ) ) @ ( sk6 @ ( arrow_411405190le_alt @ cons ) ) )
!= ( arrow_411405190le_alt @ nil @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) ) )
| ( sk5 != a )
| ~ ( A @ ( arrow_411405190le_alt @ null ) ) ),
inference(pattern_uni,[status(thm)],[1847:[]]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_append1__eq__conv) ).
thf(560,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(71,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list__nonempty__induct) ).
thf(454,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(226,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( D
= ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( B @ ( TA @ cons ) ) ) )
| ( D
= ( TA @ nil ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(232,plain,
! [TA: $tType,D: TA @ list,C: TA @ list,B: TA,A: TA @ list] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ sk2 ) ) ) ) @ ( B @ ( TA @ cons ) ) )
= D )
| ( D
= ( TA @ nil ) )
| ( ( C @ ( D @ ( TA @ append ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(45491,plain,
$false,
inference(e,[status(thm)],[384,8960,1850,555,666,352,365,138,408,9791,217,19081,449,120,202,597,174,417,288,301,1967,184,587,344,196,157,325,448,316,164,17266,8158,376,6777,10551,16776,396,411,23909,507,116,243,380,439,8959,381,220,366,302,424,429,275,165,467,229,252,197,435,9790,583,493,551,2112,324,285,519,17232,156,13576,17264,188,499,124,537,476,489,590,547,212,256,109,328,393,515,173,569,128,508,9689,558,10971,166,161,180,20447,191,579,572,1107,335,236,181,540,159,113,219,377,230,245,9789,362,451,477,552,535,609,9691,594,213,108,462,668,155,399,505,431,167,4084,278,10549,473,162,548,123,355,194,19167,640,295,414,9766,263,199,502,127,338,470,17283,10973,154,600,446,612,143,231,450,1108,482,203,171,139,21208,378,246,1193,478,272,549,207,9792,17284,262,146,190,183,373,210,107,242,341,4083,126,136,395,464,9763,596,200,178,277,442,607,309,1848,560,639,454,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT169_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/5.73 % Computer : n010.cluster.edu
% 0.25/5.73 % Model : x86_64 x86_64
% 0.25/5.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.73 % Memory : 8046.5625MB
% 0.25/5.73 % OS : Linux 6.8.0-71-generic
% 0.25/5.73 % CPULimit : 300
% 0.25/5.73 % WCLimit : 300
% 0.25/5.73 % DateTime : Sat Sep 26 06:36:36 UTC 2026
% 0.25/5.73 % CPUTime :
% 0.25/5.73 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.36/6.56 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.34/6.95 % [INFO] Parsing done (382ms).
% 2.34/6.97 % [INFO] Running in sequential loop mode.
% 3.63/7.50 % [INFO] eprover registered as external prover.
% 3.63/7.51 % [INFO] Scanning for conjecture ...
% 3.84/7.67 % [INFO] Found a conjecture (or negated_conjecture) and 104 axioms. Running axiom selection ...
% 4.02/7.78 % [INFO] Axiom selection finished. Selected 104 axioms (removed 0 axioms).
% 4.69/7.98 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.69/8.02 % [INFO] Type checking passed.
% 4.69/8.02 % [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 ...
% 109.41/29.93 % External prover 'e' found a proof!
% 109.41/29.93 % [INFO] Killing All external provers ...
% 109.41/29.93 % Time passed: 23985ms (effective reasoning time: 22953ms)
% 109.41/29.93 % 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)>
% 109.41/29.94 % Axioms used in derivation (104): fact_46_self__append__conv2, fact_52_append1__eq__conv, fact_88_dropWhile_Osimps_I1_J, fact_93_rev__swap, fact_9_not__Cons__self, fact_3_list_Oinject, fact_38_takeWhile_Osimps_I2_J, fact_16_splice_Osimps_I1_J, fact_39_append__same__eq, fact_4_distinct__length__2__or__more, fact_30_last__ConsL, fact_66_last__append, fact_23_last_Osimps, fact_1_distinct_Osimps_I1_J, fact_64_last__appendL, fact_95_takeWhile__dropWhile__id, fact_41_append__assoc, fact_32_sort__key__simps_I2_J, fact_34_append__butlast__last__id, fact_96_hd__rev, fact_67_butlast__snoc, fact_18_list_Osimps_I5_J, fact_55_append__eq__append__conv2, fact_15_splice__Nil2, fact_56_Cons__eq__appendI, fact_99_hd__append, fact_76_distinct1__rotate, fact_2_distinct__singleton, fact_69_last__snoc, arity_HOL_Obool___Orderings_Olinorder, fact_87_dropWhile_Osimps_I2_J, fact_92_distinct__dropWhile, fact_80_rev_Osimps_I2_J, fact_45_append__is__Nil__conv, fact_78_maps__simps_I2_J, fact_42_append__Cons, fact_51_distinct__sort, fact_0_alt3, fact_49_takeWhile_Osimps_I1_J, fact_77_equal__list__def, fact_47_self__append__conv, fact_61_Cons__eq__append__conv, fact_71_rev__induct, fact_6_list_Osimps_I3_J, fact_14_distinct__insert, fact_57_eq__Nil__appendI, fact_91_rev__eq__Cons__iff, fact_58_append__Nil2, fact_25_insort__key_Osimps_I1_J, fact_54_takeWhile__tail, fact_26_butlast_Osimps_I1_J, fact_79_dropWhile__eq__Cons__conv, fact_29_last__ConsR, fact_85_rev__append, fact_13_splice_Osimps_I3_J, fact_17_list_Osimps_I4_J, fact_11_insert__Nil, fact_19_list__ex1__simps_I1_J, fact_72_equal__Nil__null, fact_75_rotate1__is__Nil__conv, fact_59_append__Nil, fact_48_Nil__is__append__conv, fact_90_rev__singleton__conv, fact_89_singleton__rev__conv, fact_63_butlast__append, fact_5_list_Osimps_I2_J, fact_12_splice_Osimps_I2_J, fact_97_last__rev, fact_86_distinct__rev, fact_28_insort__not__Nil, fact_36_List_Onull__def, fact_73_rotate__simps, fact_43_append__self__conv2, fact_31_distinct__butlast, fact_7_neq__Nil__conv, fact_24_butlast_Osimps_I2_J, fact_60_distinct__takeWhile, fact_68_null__rec_I1_J, fact_84_rev__is__Nil__conv, fact_82_rev_Osimps_I1_J, fact_10_not__Cons__self2, fact_53_append__eq__appendI, fact_8_list_Oexhaust, help_pp_1_1_U, fact_37_eq__Nil__null, fact_70_rev__cases, fact_20_list__nonempty__induct, fact_27_insort__key__left__comm, fact_44_append__self__conv, fact_94_rev__rev__ident, fact_35_null__rec_I2_J, fact_65_last__appendR, fact_40_same__append__eq, fact_21_list_Orecs_I1_J, conj_0, help_pp_2_1_U, fact_50_sort__key__simps_I1_J, fact_22_list_Orecs_I2_J, fact_33_snoc__eq__iff__butlast, fact_74_maps__simps_I1_J, fact_62_append__eq__Cons__conv, fact_83_Nil__is__rev__conv, fact_98_hd_Osimps, fact_81_rev__is__rev__conv
% 109.41/29.94 % No. of inferences in proof: 572
% 109.41/29.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23985 ms resp. 22953 ms w/o parsing
% 110.14/30.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 110.14/30.12 % [INFO] Killing All external provers ...
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