%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL764_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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:47 AM UTC 2026
% Result : Theorem 9.29s 4.06s
% Output : Refutation 9.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 114
% Syntax : Number of formulae : 230 ( 94 unt; 0 typ; 0 def)
% Number of atoms : 613 ( 402 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 3046 ( 76 ~; 19 |; 94 &;2672 @)
% ( 31 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 7 con; 0-5 aty)
% Number of variables : 683 ( 0 ^; 662 !; 21 ?; 683 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(enum_decl,type,
enum:
!>[TA: $tType] : $o ).
thf(cl_HOL_Oequal_decl,type,
cl_HOL_Oequal:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(product_decl,type,
product:
!>[TA: $tType,TB: $tType] : ( ( TB @ list ) > ( TA @ list ) > ( TA @ ( TB @ product_prod ) @ list ) ) ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(lift_decl,type,
lift: dB > nat > dB ).
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(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(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(listsp_decl,type,
listsp:
!>[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(member_decl,type,
member:
!>[TA: $tType] : ( ( TA @ list ) > TA > $o ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(replicate_decl,type,
replicate:
!>[TA: $tType] : ( nat > TA > ( TA @ list ) ) ).
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(tl_decl,type,
tl:
!>[TA: $tType] : ( ( 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(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(69,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ listsp ) ) )
<=> ( ? [C: TA,D: TA @ list] :
( ( D @ ( B @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( TA @ cons ) ) ) ) )
| ( A
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_listsp_Osimps) ).
thf(385,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ( ? [C: TA,D: TA @ list] :
( ( D @ ( B @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( TA @ cons ) ) ) ) )
| ( A
= ( TA @ nil ) ) )
=> ( A @ ( B @ ( TA @ listsp ) ) ) )
& ( ( A @ ( B @ ( TA @ listsp ) ) )
=> ( ? [C: TA,D: TA @ list] :
( ( D @ ( B @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( TA @ cons ) ) ) ) )
| ( A
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(111,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_splice_Osimps_I1_J) ).
thf(610,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(107,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_10_maps__simps_I2_J) ).
thf(586,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)],[107]) ).
thf(32,axiom,
! [TA: $tType,A: nat,B: TA,C: nat] :
( ( B @ ( A @ ( TA @ replicate ) ) @ ( B @ ( C @ ( TA @ replicate ) ) @ ( TA @ append ) ) )
= ( B @ ( C @ ( TA @ replicate ) ) @ ( B @ ( A @ ( TA @ replicate ) ) @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_append__replicate__commute) ).
thf(231,plain,
! [TA: $tType,A: nat,B: TA,C: nat] :
( ( B @ ( A @ ( TA @ replicate ) ) @ ( B @ ( C @ ( TA @ replicate ) ) @ ( TA @ append ) ) )
= ( B @ ( C @ ( TA @ replicate ) ) @ ( B @ ( A @ ( TA @ replicate ) ) @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(115,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_46_append__self__conv2) ).
thf(632,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)],[115]) ).
thf(65,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_49_self__append__conv2) ).
thf(365,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)],[65]) ).
thf(97,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_73_rev_Osimps_I2_J) ).
thf(518,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)],[97]) ).
thf(33,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_43_same__append__eq) ).
thf(234,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)],[33]) ).
thf(57,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_list__ex1__simps_I1_J) ).
thf(333,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(35,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_45_append__Cons) ).
thf(249,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)],[35]) ).
thf(87,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_null__rec_I2_J) ).
thf(481,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(62,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_64_last__appendR) ).
thf(352,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)],[62]) ).
thf(78,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Nil__is__rev__conv) ).
thf(440,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)],[78]) ).
thf(27,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(217,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)],[27]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ fequal )
= ( TA @ equal_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_eq__equal) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ fequal )
= ( TA @ equal_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(13,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_79_rev__append) ).
thf(174,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)],[13]) ).
thf(54,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(320,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)],[54]) ).
thf(38,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_54_append__eq__appendI) ).
thf(257,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)],[38]) ).
thf(103,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_2_list_Osimps_I4_J) ).
thf(570,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)],[103]) ).
thf(66,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(372,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)],[66]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( A @ ( B @ ( TA @ replicate ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ replicate ) ) @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_replicate__append__same) ).
thf(504,plain,
! [TA: $tType,A: TA,B: nat] :
( ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( A @ ( B @ ( TA @ replicate ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ replicate ) ) @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ equal_equal )
= ( TA @ fequal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_equal) ).
thf(196,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ equal_equal )
= ( TA @ fequal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,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_62_butlast__append) ).
thf(416,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)],[74]) ).
thf(31,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_44_append__assoc) ).
thf(228,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)],[31]) ).
thf(80,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_81_singleton__rev__conv) ).
thf(448,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)],[80]) ).
thf(39,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ hd ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_hd_Osimps) ).
thf(261,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ hd ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(11,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_85_rev__swap) ).
thf(164,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)],[11]) ).
thf(67,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_member__rec_I2_J) ).
thf(376,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(24,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_not__Cons__self2) ).
thf(211,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(221,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1,conjecture,
dB @ nil @ ( it @ ( dB @ listsp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( dB @ nil @ ( it @ ( dB @ listsp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(116,plain,
~ ( dB @ nil @ ( it @ ( dB @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(94,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_35_last__ConsR) ).
thf(507,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)],[94]) ).
thf(22,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(206,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( A @ ( TA @ hd ) @ ( TA @ cons ) ) @ ( A @ ( TA @ tl ) @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rotate1__hd__tl) ).
thf(307,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( A @ ( TA @ hd ) @ ( TA @ cons ) ) @ ( A @ ( TA @ tl ) @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(48,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list_Osimps_I3_J) ).
thf(292,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3,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_12_list_Oinject) ).
thf(117,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)],[3]) ).
thf(42,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_17_list_Osimps_I5_J) ).
thf(270,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)],[42]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list_Osimps_I2_J) ).
thf(349,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_equal__eq) ).
thf(137,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_null__rec_I1_J) ).
thf(252,plain,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(114,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_83_rev__eq__Cons__iff) ).
thf(625,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)],[114]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ tl ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_tl_Osimps_I1_J) ).
thf(583,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ tl ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
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_99_insort__key_Osimps_I1_J) ).
thf(551,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(47,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_eq__Nil__null) ).
thf(285,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)],[47]) ).
thf(85,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_append__Nil2) ).
thf(471,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ replicate ) ) @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ replicate ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rev__replicate) ).
thf(225,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ replicate ) ) @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ replicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(102,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_60_append__eq__Cons__conv) ).
thf(554,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)],[102]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_not__Cons__self) ).
thf(193,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(113,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_87_last__rev) ).
thf(622,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)],[113]) ).
thf(96,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_68_last__snoc) ).
thf(515,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)],[96]) ).
thf(5,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_42_append__same__eq) ).
thf(129,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)],[5]) ).
thf(50,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_51_Nil__is__append__conv) ).
thf(298,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)],[50]) ).
thf(73,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_69_rev__induct) ).
thf(412,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)],[73]) ).
thf(76,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_86_hd__rev) ).
thf(430,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)],[76]) ).
thf(40,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_66_maps__simps_I1_J) ).
thf(264,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)],[40]) ).
thf(45,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ tl ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_tl_Osimps_I2_J) ).
thf(279,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ tl ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(104,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_65_last__append) ).
thf(573,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)],[104]) ).
thf(16,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_74_rev__is__rev__conv) ).
thf(180,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)],[16]) ).
thf(75,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rotate1__is__Nil__conv) ).
thf(423,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)],[75]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(191,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,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_50_self__append__conv) ).
thf(313,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)],[53]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ cl_HOL_Oequal ) )
=> ( TA @ ( TB @ fun ) @ cl_HOL_Oequal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(144,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ cl_HOL_Oequal ) )
=> ( TA @ ( TB @ fun ) @ cl_HOL_Oequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ tl ) )
= ( A @ ( B @ ( TA @ tl ) @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_tl__append2) ).
thf(466,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ tl ) )
= ( A @ ( B @ ( TA @ tl ) @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(58,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_listsp_ONil) ).
thf(335,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(187,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(71,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_71_rev__exhaust2) ).
thf(406,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)],[71]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ product_prod ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Enum_Oenum) ).
thf(172,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ product_prod ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,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_5_list_Orecs_I1_J) ).
thf(362,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)],[64]) ).
thf(23,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: nat] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( C @ ( TA @ replicate ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( C @ ( TA @ replicate ) ) @ ( TA @ append ) ) @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_replicate__app__Cons__same) ).
thf(208,plain,
! [TA: $tType,A: TA @ list,B: TA,C: nat] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( C @ ( TA @ replicate ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( C @ ( TA @ replicate ) ) @ ( TA @ append ) ) @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,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_25_splice_Osimps_I2_J) ).
thf(494,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)],[90]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_butlast_Osimps_I1_J) ).
thf(323,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(88,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_equal__Nil__null) ).
thf(483,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( TA @ nil @ ( A @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
& ( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(98,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_72_rotate__simps) ).
thf(521,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)],[98]) ).
thf(70,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_rev__is__Nil__conv) ).
thf(399,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)],[70]) ).
thf(81,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_21_list_Oexhaust) ).
thf(455,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)],[81]) ).
thf(41,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_18_list_Orecs_I2_J) ).
thf(267,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)],[41]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member ) ) )
<=> ( ( A @ ( B @ ( TA @ member ) ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_member__rec_I1_J) ).
thf(241,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( ( ( A @ ( B @ ( TA @ member ) ) )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ member ) ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(108,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_37_snoc__eq__iff__butlast) ).
thf(589,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)],[108]) ).
thf(10,axiom,
! [TA: $tType] : ( TA @ list @ cl_HOL_Oequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___HOL_Oequal) ).
thf(162,plain,
! [TA: $tType] : ( TA @ list @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,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_28_last_Osimps) ).
thf(487,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)],[89]) ).
thf(63,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_82_rev__singleton__conv) ).
thf(355,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)],[63]) ).
thf(82,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_27_list__nonempty__induct) ).
thf(458,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)],[82]) ).
thf(105,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_splice__Nil2) ).
thf(580,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(49,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(295,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)],[49]) ).
thf(46,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_append__Nil) ).
thf(282,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: TB @ list] :
( ( A @ ( TA @ nil @ ( TB @ ( TA @ product ) ) ) )
= ( TB @ ( TA @ product_prod ) @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_product_Osimps_I1_J) ).
thf(409,plain,
! [TA: $tType,TB: $tType,A: TB @ list] :
( ( A @ ( TA @ nil @ ( TB @ ( TA @ product ) ) ) )
= ( TB @ ( TA @ product_prod ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rev_Osimps_I1_J) ).
thf(310,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_equal__list__def) ).
thf(199,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
bool @ enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(177,plain,
bool @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(100,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_29_butlast_Osimps_I2_J) ).
thf(544,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)],[100]) ).
thf(112,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_48_append__is__Nil__conv) ).
thf(613,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)],[112]) ).
thf(91,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_63_last__appendL) ).
thf(497,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)],[91]) ).
thf(68,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_90_hd__append) ).
thf(378,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)],[68]) ).
thf(60,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__Nil) ).
thf(346,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(25,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(214,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(77,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_47_append__self__conv) ).
thf(433,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)],[77]) ).
thf(95,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ listsp ) ) )
<=> ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_append__in__listsp__conv) ).
thf(510,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) )
=> ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ listsp ) ) ) )
& ( ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ listsp ) ) )
=> ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
dB @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Lambda_OdB___HOL_Oequal) ).
thf(447,plain,
dB @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(9,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)],[9]) ).
thf(43,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_rev__rev__ident) ).
thf(273,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(109,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_34_last__ConsL) ).
thf(603,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)],[109]) ).
thf(56,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_22_neq__Nil__conv) ).
thf(326,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)],[56]) ).
thf(86,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_List_Onull__def) ).
thf(474,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)],[86]) ).
thf(4,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_26_splice_Osimps_I3_J) ).
thf(126,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)],[4]) ).
thf(6,axiom,
bool @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(136,plain,
bool @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(99,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(528,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)],[99]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA] : ( A @ ( A @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_equal__refl) ).
thf(178,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA] : ( A @ ( A @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(92,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_36_append__butlast__last__id) ).
thf(501,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)],[92]) ).
thf(110,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ hd ) )
= ( B @ ( TA @ hd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_hd__append2) ).
thf(607,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ hd ) )
= ( B @ ( TA @ hd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(254,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(59,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_53_append1__eq__conv) ).
thf(337,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)],[59]) ).
thf(84,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_lift__IT) ).
thf(469,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] : ( TA @ ( TB @ product_prod ) @ cl_HOL_Oequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___HOL_Oequal) ).
thf(215,plain,
! [TA: $tType,TB: $tType] : ( TA @ ( TB @ product_prod ) @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(639,plain,
$false,
inference(e,[status(thm)],[385,610,586,231,632,365,518,234,333,249,481,352,440,217,276,174,320,257,570,372,504,196,416,228,448,261,164,376,211,221,116,507,206,307,292,117,270,349,137,252,625,583,551,285,471,225,554,193,622,515,129,298,412,430,264,279,573,180,423,191,313,144,466,335,187,406,172,362,208,494,323,483,521,399,455,267,241,589,162,487,355,458,580,295,282,409,310,199,177,544,613,497,378,346,214,433,510,447,146,273,603,326,474,126,136,528,178,501,607,254,337,469,215,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL764_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.13/0.54 % Computer : n005.cluster.edu
% 0.13/0.54 % Model : x86_64 x86_64
% 0.13/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.54 % Memory : 8046.5625MB
% 0.13/0.54 % OS : Linux 6.8.0-71-generic
% 0.13/0.54 % CPULimit : 300
% 0.13/0.54 % WCLimit : 300
% 0.13/0.54 % DateTime : Fri Sep 25 23:31:17 UTC 2026
% 0.13/0.55 % CPUTime :
% 0.13/0.55 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
% 1.00/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.44 % [INFO] Parsing done (303ms).
% 1.64/1.46 % [INFO] Running in sequential loop mode.
% 2.47/1.84 % [INFO] eprover registered as external prover.
% 2.47/1.85 % [INFO] Scanning for conjecture ...
% 2.67/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 113 axioms. Running axiom selection ...
% 2.89/2.11 % [INFO] Axiom selection finished. Selected 113 axioms (removed 0 axioms).
% 3.52/2.33 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.52/2.36 % [INFO] Type checking passed.
% 3.52/2.37 % [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 ...
% 9.29/4.06 % External prover 'e' found a proof!
% 9.29/4.06 % [INFO] Killing All external provers ...
% 9.29/4.06 % Time passed: 3371ms (effective reasoning time: 2598ms)
% 9.29/4.06 % 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)>
% 9.29/4.06 % Axioms used in derivation (113): fact_6_null__rec_I2_J, fact_89_hd__append2, fact_9_listsp_Osimps, fact_49_self__append__conv2, fact_69_rev__induct, fact_8_eq__Nil__null, fact_94_rev__replicate, arity_prod___HOL_Oequal, fact_66_maps__simps_I1_J, fact_2_list_Osimps_I4_J, fact_39_equal__eq, fact_25_splice_Osimps_I2_J, fact_80_rotate1__is__Nil__conv, fact_99_insort__key_Osimps_I1_J, arity_fun___HOL_Oequal, fact_10_maps__simps_I2_J, fact_76_rev_Osimps_I1_J, fact_23_insert__Nil, fact_91_rotate1__hd__tl, fact_63_last__appendL, fact_43_same__append__eq, fact_98_append__replicate__commute, fact_13_not__Cons__self, fact_67_butlast__snoc, fact_65_last__append, fact_5_list_Orecs_I1_J, fact_48_append__is__Nil__conv, fact_88_hd_Osimps, fact_28_last_Osimps, fact_40_equal__refl, fact_55_append__eq__append__conv2, fact_46_append__self__conv2, fact_15_null__rec_I1_J, fact_31_equal__list__def, fact_56_Cons__eq__appendI, arity_HOL_Obool___HOL_Oequal, fact_77_Nil__is__rev__conv, arity_HOL_Obool___Orderings_Olinorder, fact_79_rev__append, arity_fun___Enum_Oenum, fact_93_tl_Osimps_I1_J, fact_84_rev__rev__ident, fact_51_Nil__is__append__conv, fact_4_list__ex1__simps_I1_J, fact_87_last__rev, fact_12_list_Oinject, fact_22_neq__Nil__conv, fact_71_rev__exhaust2, fact_50_self__append__conv, fact_24_equal__Nil__null, fact_26_splice_Osimps_I3_J, fact_42_append__same__eq, fact_54_append__eq__appendI, fact_30_butlast_Osimps_I1_J, fact_90_hd__append, fact_18_list_Orecs_I2_J, arity_HOL_Obool___Enum_Oenum, arity_List_Olist___HOL_Oequal, fact_61_Cons__eq__append__conv, fact_27_list__nonempty__induct, fact_64_last__appendR, fact_36_append__butlast__last__id, fact_32_splice_Osimps_I1_J, fact_57_eq__Nil__appendI, fact_58_append__Nil2, fact_62_butlast__append, fact_52_append__in__listsp__conv, fact_16_member__rec_I1_J, fact_47_append__self__conv, fact_83_rev__eq__Cons__iff, fact_7_List_Onull__def, fact_59_append__Nil, fact_96_tl__append2, arity_prod___Enum_Oenum, help_fequal_1_1_T, arity_Lambda_OdB___HOL_Oequal, fact_0_listsp_ONil, fact_82_rev__singleton__conv, fact_33_splice__Nil2, fact_14_not__Cons__self2, fact_72_rotate__simps, fact_21_list_Oexhaust, fact_3_product_Osimps_I1_J, fact_37_snoc__eq__iff__butlast, fact_60_append__eq__Cons__conv, fact_68_last__snoc, fact_45_append__Cons, help_fequal_2_1_T, fact_81_singleton__rev__conv, fact_11_member__rec_I2_J, fact_38_eq__equal, fact_97_tl_Osimps_I2_J, fact_78_rev__is__Nil__conv, fact_73_rev_Osimps_I2_J, fact_19_list_Osimps_I3_J, help_pp_1_1_U, fact_44_append__assoc, fact_70_rev__cases, fact_41_equal, fact_85_rev__swap, fact_92_replicate__append__same, fact_95_replicate__app__Cons__same, fact_53_append1__eq__conv, fact_17_list_Osimps_I5_J, fact_75_ext, help_pp_2_1_U, fact_1_lift__IT, fact_35_last__ConsR, fact_86_hd__rev, fact_29_butlast_Osimps_I2_J, fact_74_rev__is__rev__conv, fact_20_list_Osimps_I2_J, fact_34_last__ConsL
% 9.29/4.06 % No. of inferences in proof: 230
% 9.29/4.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3371 ms resp. 2598 ms w/o parsing
% 9.96/4.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.96/4.21 % [INFO] Killing All external provers ...
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