TSTP Solution File: SCT169_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT169_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:56 EDT 2023
% Result : Theorem 82.23s 16.17s
% Output : Refutation 82.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 135
% Syntax : Number of formulae : 242 ( 84 unt; 30 typ; 0 def)
% Number of atoms : 548 ( 387 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 3110 ( 78 ~; 9 |; 93 &;2736 @)
% ( 32 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 7 con; 0-5 aty)
% Number of variables : 701 ( 0 ^; 648 !; 24 ?; 701 :)
% ( 29 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(equal_equal_type,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(butlast_type,type,
butlast:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(distinct_type,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(dropWhile_type,type,
dropWhile:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(hd_type,type,
hd:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(linorder_insort_key_type,type,
linorder_insort_key:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > ( list @ TB ) > ( list @ TB ) ) ).
thf(linorder_sort_key_type,type,
linorder_sort_key:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( list @ TB ) > ( list @ TB ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_rec_type,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) ) > ( list @ TA ) > TB ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(maps_type,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(null_type,type,
null:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(rev_type,type,
rev:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(rotate1_type,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(takeWhile_type,type,
takeWhile:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(83,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_splice_Osimps_I3_J) ).
thf(468,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(9,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( rev @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ ( rev @ TA @ A ) @ ( rev @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rev__append) ).
thf(133,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( rev @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ ( rev @ TA @ A ) @ ( rev @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ B @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_equal__list__def) ).
thf(169,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( equal_equal @ ( list @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( rev @ TA @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) )
<=> ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_rev__singleton__conv) ).
thf(503,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( ( rev @ TA @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) )
=> ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) )
=> ( ( rev @ TA @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(68,axiom,
! [TA: $tType,A: list @ TA] :
( ( null @ TA @ A )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_List_Onull__def) ).
thf(413,plain,
! [TA: $tType,A: list @ TA] :
( ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(47,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( rev @ TA @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_hd__rev) ).
thf(331,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( rev @ TA @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(4,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ B )
= ( rev @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rev__is__rev__conv) ).
thf(115,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( rev @ TA @ B )
= ( rev @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( rev @ TA @ B )
= ( rev @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(92,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( takeWhile @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_takeWhile_Osimps_I1_J) ).
thf(511,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( takeWhile @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( butlast @ TA @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_butlast__snoc) ).
thf(202,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( butlast @ TA @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(98,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ B @ A )
= A )
<=> ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_append__self__conv2) ).
thf(533,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( append @ TA @ B @ A )
= A )
=> ( B
= ( nil @ TA ) ) )
& ( ( B
= ( nil @ TA ) )
=> ( ( append @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
<=> ? [E: list @ TA] :
( ( ( D
= ( append @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) )
| ( ( ( append @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_append__eq__append__conv2) ).
thf(142,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( append @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
=> ? [E: list @ TA] :
( ( ( D
= ( append @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) )
| ( ( ( append @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) )
& ( ? [E: list @ TA] :
( ( ( D
= ( append @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) )
| ( ( ( append @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) )
=> ( ( append @ TA @ D @ C )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: fun @ TA @ TB] :
( ( linorder_sort_key @ TA @ TB @ A @ ( nil @ TA ) )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_sort__key__simps_I1_J) ).
thf(500,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: fun @ TA @ TB] :
( ( linorder_sort_key @ TA @ TB @ A @ ( nil @ TA ) )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(49,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( takeWhile @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_distinct__takeWhile) ).
thf(340,plain,
! [TA: $tType,A: fun @ TA @ bool,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( takeWhile @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: fun @ TA @ TB] :
( ( distinct @ TA @ ( linorder_sort_key @ TA @ TB @ B @ A ) )
<=> ( distinct @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_distinct__sort) ).
thf(404,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: fun @ TA @ TB] :
( ( ( distinct @ TA @ ( linorder_sort_key @ TA @ TB @ B @ A ) )
=> ( distinct @ TA @ A ) )
& ( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( linorder_sort_key @ TA @ TB @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(106,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( dropWhile @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dropWhile_Osimps_I1_J) ).
thf(565,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( dropWhile @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(74,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_splice_Osimps_I2_J) ).
thf(436,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( linorder_insort_key @ TA @ TB @ C @ B @ A )
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insort__not__Nil) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( linorder_insort_key @ TA @ TB @ C @ B @ A )
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(19,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_append__Nil) ).
thf(184,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(58,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_append__Nil2) ).
thf(372,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(23,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( rev @ TA @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Nil__is__rev__conv) ).
thf(196,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( nil @ TA )
= ( rev @ TA @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( nil @ TA )
= ( rev @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(125,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA] :
( ( ( rotate1 @ TB @ ( nil @ TB ) )
= ( nil @ TB ) )
& ( ( rotate1 @ TA @ ( cons @ TA @ B @ A ) )
= ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rotate__simps) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA] :
( ( ( rotate1 @ TB @ ( nil @ TB ) )
= ( nil @ TB ) )
& ( ( rotate1 @ TA @ ( cons @ TA @ B @ A ) )
= ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( dropWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( dropWhile @ TA @ C @ A ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( dropWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dropWhile_Osimps_I2_J) ).
thf(460,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( dropWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( dropWhile @ TA @ C @ A ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( dropWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ C @ B ) @ A )
= ( append @ TA @ C @ ( append @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_append__assoc) ).
thf(157,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ C @ B ) @ A )
= ( append @ TA @ C @ ( append @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
= ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_eq__Nil__null) ).
thf(559,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(70,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( hd @ TA @ ( cons @ TA @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_hd_Osimps) ).
thf(421,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( hd @ TA @ ( cons @ TA @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(34,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_not__Cons__self2) ).
thf(261,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(45,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( rev @ TA @ ( cons @ TA @ B @ A ) )
= ( append @ TA @ ( rev @ TA @ A ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rev_Osimps_I2_J) ).
thf(321,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( rev @ TA @ ( cons @ TA @ B @ A ) )
= ( append @ TA @ ( rev @ TA @ A ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(26,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( ( D
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ B @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( cons @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_append__eq__Cons__conv) ).
thf(211,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ( ( append @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( ( D
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ B @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( cons @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) ) ) )
& ( ( ( ( D
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ B @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( cons @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) ) )
=> ( ( append @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(53,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_distinct__singleton) ).
thf(353,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(86,axiom,
! [TA: $tType,A: list @ TA,B: fun @ ( list @ TA ) @ bool] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rev__induct) ).
thf(480,plain,
! [TA: $tType,A: list @ TA,B: fun @ ( list @ TA ) @ bool] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(5,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(121,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_list_Osimps_I3_J) ).
thf(514,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(75,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( append @ TA @ ( cons @ TA @ C @ B ) @ A )
= ( cons @ TA @ C @ ( append @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_append__Cons) ).
thf(439,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( append @ TA @ ( cons @ TA @ C @ B ) @ A )
= ( cons @ TA @ C @ ( append @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(36,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ D @ C ) )
=> ( ( takeWhile @ TA @ D @ ( append @ TA @ B @ ( cons @ TA @ C @ A ) ) )
= ( takeWhile @ TA @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_takeWhile__tail) ).
thf(270,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ D @ C ) )
=> ( ( takeWhile @ TA @ D @ ( append @ TA @ B @ ( cons @ TA @ C @ A ) ) )
= ( takeWhile @ TA @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: fun @ TA @ TB] :
( ( linorder_insort_key @ TA @ TB @ B @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insort__key_Osimps_I1_J) ).
thf(546,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: fun @ TA @ TB] :
( ( linorder_insort_key @ TA @ TB @ B @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ A ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_last__append) ).
thf(334,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ A ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(13,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(160,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(63,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ A @ B ) )
= ( butlast @ TA @ A ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ A @ ( butlast @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_butlast__append) ).
thf(392,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ A @ B ) )
= ( butlast @ TA @ A ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ A @ ( butlast @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list__nonempty__induct) ).
thf(424,plain,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_equal__Nil__null) ).
thf(407,plain,
! [TA: $tType,A: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
<=> ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_distinct__length__2__or__more) ).
thf(361,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
=> ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) )
& ( ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_append1__eq__conv) ).
thf(522,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(80,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( ( ( cons @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( cons @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Cons__eq__appendI) ).
thf(456,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( ( ( cons @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( cons @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: fun @ TA @ bool] :
( ( ( dropWhile @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( C
= ( append @ TA @ ( takeWhile @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) ) )
& ~ ( pp @ ( aa @ TA @ bool @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_dropWhile__eq__Cons__conv) ).
thf(324,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: fun @ TA @ bool] :
( ( ( ( dropWhile @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( C
= ( append @ TA @ ( takeWhile @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) ) )
& ~ ( pp @ ( aa @ TA @ bool @ D @ B ) ) ) )
& ( ( ( C
= ( append @ TA @ ( takeWhile @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) ) )
& ~ ( pp @ ( aa @ TA @ bool @ D @ B ) ) )
=> ( ( dropWhile @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ C @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= A )
<=> ( ( A
!= ( nil @ TA ) )
& ( ( butlast @ TA @ A )
= C )
& ( ( last @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_snoc__eq__iff__butlast) ).
thf(285,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= A )
=> ( ( A
!= ( nil @ TA ) )
& ( ( butlast @ TA @ A )
= C )
& ( ( last @ TA @ A )
= B ) ) )
& ( ( ( A
!= ( nil @ TA ) )
& ( ( butlast @ TA @ A )
= C )
& ( ( last @ TA @ A )
= B ) )
=> ( ( append @ TA @ C @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_last__ConsR) ).
thf(193,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_same__append__eq) ).
thf(109,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(84,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list_Osimps_I2_J) ).
thf(471,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(31,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_neq__Nil__conv) ).
thf(244,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( rev @ TA @ C )
= ( cons @ TA @ B @ A ) )
<=> ( C
= ( append @ TA @ ( rev @ TA @ A ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rev__eq__Cons__iff) ).
thf(205,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( ( rev @ TA @ C )
= ( cons @ TA @ B @ A ) )
=> ( C
= ( append @ TA @ ( rev @ TA @ A ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) )
& ( ( C
= ( append @ TA @ ( rev @ TA @ A ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
=> ( ( rev @ TA @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ A @ B ) )
= ( nil @ TA ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ A @ B ) )
= ( cons @ TA @ A @ ( butlast @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_butlast_Osimps_I2_J) ).
thf(398,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ A @ B ) )
= ( nil @ TA ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ A @ B ) )
= ( cons @ TA @ A @ ( butlast @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(97,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Oexhaust) ).
thf(530,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(40,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ B @ A )
= ( nil @ TA ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_append__is__Nil__conv) ).
thf(298,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( append @ TA @ B @ A )
= ( nil @ TA ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( append @ TA @ B @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( append @ TA @ ( takeWhile @ TA @ B @ A ) @ ( dropWhile @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_takeWhile__dropWhile__id) ).
thf(166,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( append @ TA @ ( takeWhile @ TA @ B @ A ) @ ( dropWhile @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(35,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( rev @ TA @ A ) )
<=> ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_singleton__rev__conv) ).
thf(264,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( rev @ TA @ A ) )
=> ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) )
& ( ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( rev @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rotate1__is__Nil__conv) ).
thf(279,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( rotate1 @ TA @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ B @ A ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Nil__is__append__conv) ).
thf(375,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( nil @ TA )
= ( append @ TA @ B @ A ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( nil @ TA )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(77,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_distinct_Osimps_I1_J) ).
thf(445,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(88,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_distinct__insert) ).
thf(498,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( list @ TB )] :
( ( maps @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( append @ TB @ ( aa @ TA @ ( list @ TB ) @ C @ B ) @ ( maps @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_maps__simps_I1_J) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( list @ TB )] :
( ( maps @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( append @ TB @ ( aa @ TA @ ( list @ TB ) @ C @ B ) @ ( maps @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_list_Orecs_I2_J) ).
thf(187,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(69,axiom,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_alt3) ).
thf(419,plain,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list_Osimps_I5_J) ).
thf(318,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list__ex1__simps_I1_J) ).
thf(509,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(87,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
<=> ( ( ( B
= ( nil @ TA ) )
& ( ( cons @ TA @ D @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Cons__eq__append__conv) ).
thf(483,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
=> ( ( ( B
= ( nil @ TA ) )
& ( ( cons @ TA @ D @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) )
& ( ( ( ( B
= ( nil @ TA ) )
& ( ( cons @ TA @ D @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) )
=> ( ( cons @ TA @ D @ C )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(95,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( dropWhile @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_distinct__dropWhile) ).
thf(520,plain,
! [TA: $tType,A: fun @ TA @ bool,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( dropWhile @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_last__ConsL) ).
thf(240,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_append__butlast__last__id) ).
thf(306,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( append @ TA @ B @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_self__append__conv) ).
thf(226,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( append @ TA @ B @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(72,axiom,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_null__rec_I2_J) ).
thf(431,plain,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(14,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( append @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_append__eq__appendI) ).
thf(162,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( append @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_null__rec_I1_J) ).
thf(342,plain,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(54,axiom,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_butlast_Osimps_I1_J) ).
thf(355,plain,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(103,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(553,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: TA,D: fun @ TA @ TB] :
( ( ( aa @ TA @ TB @ D @ C )
!= ( aa @ TA @ TB @ D @ B ) )
=> ( ( linorder_insort_key @ TA @ TB @ D @ B @ ( linorder_insort_key @ TA @ TB @ D @ C @ A ) )
= ( linorder_insort_key @ TA @ TB @ D @ C @ ( linorder_insort_key @ TA @ TB @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insort__key__left__comm) ).
thf(175,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: TA,D: fun @ TA @ TB] :
( ( ( aa @ TA @ TB @ D @ C )
!= ( aa @ TA @ TB @ D @ B ) )
=> ( ( linorder_insort_key @ TA @ TB @ D @ B @ ( linorder_insort_key @ TA @ TB @ D @ C @ A ) )
= ( linorder_insort_key @ TA @ TB @ D @ C @ ( linorder_insort_key @ TA @ TB @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list_Orecs_I1_J) ).
thf(386,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(79,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ B @ A ) )
= ( hd @ TA @ A ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ B @ A ) )
= ( hd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_hd__append) ).
thf(450,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ B @ A ) )
= ( hd @ TA @ A ) ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ B @ A ) )
= ( hd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(104,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rev__cases) ).
thf(556,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_last__appendL) ).
thf(539,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(32,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list_Oinject) ).
thf(250,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(82,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_splice_Osimps_I1_J) ).
thf(465,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( rev @ TA @ A ) )
= ( hd @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_last__rev) ).
thf(517,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( rev @ TA @ A ) )
= ( hd @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( last @ TA @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_last__snoc) ).
thf(258,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( last @ TA @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(29,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( takeWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( takeWhile @ TA @ C @ A ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( takeWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_takeWhile_Osimps_I2_J) ).
thf(235,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( takeWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( takeWhile @ TA @ C @ A ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( takeWhile @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(73,axiom,
! [TA: $tType] :
( ( rev @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rev_Osimps_I1_J) ).
thf(433,plain,
! [TA: $tType] :
( ( rev @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( linorder_sort_key @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( linorder_insort_key @ TA @ TB @ C @ B @ ( linorder_sort_key @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_sort__key__simps_I2_J) ).
thf(383,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( linorder_sort_key @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( linorder_insort_key @ TA @ TB @ C @ B @ ( linorder_sort_key @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B = A )
=> ( B
= ( append @ TA @ ( nil @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_eq__Nil__appendI) ).
thf(549,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B = A )
=> ( B
= ( append @ TA @ ( nil @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA] :
( ( distinct @ TA @ ( rev @ TA @ A ) )
<=> ( distinct @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_distinct__rev) ).
thf(447,plain,
! [TA: $tType,A: list @ TA] :
( ( ( distinct @ TA @ ( rev @ TA @ A ) )
=> ( distinct @ TA @ A ) )
& ( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( rev @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list_Osimps_I4_J) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(67,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( butlast @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_distinct__butlast) ).
thf(410,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( butlast @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(21,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_splice__Nil2) ).
thf(190,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ B @ A )
= B )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_append__self__conv) ).
thf(273,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( append @ TA @ B @ A )
= B )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( append @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1,conjecture,
? [A: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ? [A: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(107,plain,
~ ? [A: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_last__appendR) ).
thf(358,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rev @ TA @ A )
= ( nil @ TA ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_rev__is__Nil__conv) ).
thf(474,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( rev @ TA @ A )
= ( nil @ TA ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( rev @ TA @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(8,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ B )
= A )
<=> ( B
= ( rev @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rev__swap) ).
thf(126,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( rev @ TA @ B )
= A )
=> ( B
= ( rev @ TA @ A ) ) )
& ( ( B
= ( rev @ TA @ A ) )
=> ( ( rev @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_append__same__eq) ).
thf(136,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( append @ TA @ A @ B ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_self__append__conv2) ).
thf(178,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( append @ TA @ A @ B ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(76,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_insert__Nil) ).
thf(442,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_maps__simps_I2_J) ).
thf(369,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rev__rev__ident) ).
thf(122,plain,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= A ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_last_Osimps) ).
thf(309,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( B
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= A ) )
& ( ( B
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(100,axiom,
! [TA: $tType,A: list @ TA] :
( ( distinct @ TA @ ( rotate1 @ TA @ A ) )
<=> ( distinct @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_distinct1__rotate) ).
thf(543,plain,
! [TA: $tType,A: list @ TA] :
( ( ( distinct @ TA @ ( rotate1 @ TA @ A ) )
=> ( distinct @ TA @ A ) )
& ( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( rotate1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_not__Cons__self) ).
thf(232,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(51393,plain,
$false,
inference(e,[status(thm)],[468,133,169,503,413,331,115,511,202,533,142,500,340,404,565,436,389,184,372,196,125,344,460,157,559,421,261,321,211,353,480,121,514,439,270,546,334,160,392,424,407,361,522,456,324,285,193,109,471,244,205,398,530,298,166,264,279,375,445,498,350,187,419,318,509,483,520,240,306,226,431,162,342,355,553,175,386,450,556,539,250,465,517,258,235,433,383,549,447,315,410,190,273,107,358,474,126,136,178,442,369,122,309,543,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SCT169_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:27:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.10 % [INFO] Parsing done (200ms).
% 1.63/1.10 % [INFO] Running in sequential loop mode.
% 2.21/1.31 % [INFO] eprover registered as external prover.
% 2.21/1.31 % [INFO] cvc4 registered as external prover.
% 2.21/1.32 % [INFO] Scanning for conjecture ...
% 2.52/1.41 % [INFO] Found a conjecture and 104 axioms. Running axiom selection ...
% 2.71/1.47 % [INFO] Axiom selection finished. Selected 104 axioms (removed 0 axioms).
% 3.14/1.60 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.14/1.61 % [INFO] Type checking passed.
% 3.14/1.61 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 82.08/16.16 % External prover 'e' found a proof!
% 82.08/16.16 % [INFO] Killing All external provers ...
% 82.23/16.16 % Time passed: 15630ms (effective reasoning time: 15055ms)
% 82.23/16.16 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 82.23/16.17 % 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
% 82.23/16.17 % No. of inferences in proof: 212
% 82.23/16.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 15630 ms resp. 15055 ms w/o parsing
% 82.23/16.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 82.23/16.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------