%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL769_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 : n019.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 07:52:48 AM UTC 2026
% Result : Theorem 39.73s 23.91s
% Output : Refutation 41.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 117
% Syntax : Number of formulae : 236 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 2268 ( 447 equ; 0 cnn)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 7614 ( 108 ~; 38 |; 130 &;7151 @)
% ( 35 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 12 con; 0-5 aty)
% Number of variables : 804 ( 0 ^; 772 !; 32 ?; 804 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) @ ( TB @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(abs_decl,type,
abs: dB > dB ).
thf(app_decl,type,
app: dB @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_case_decl,type,
dB_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( dB @ fun ) ) > dB > TA ) ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) ) ).
thf(butlast_decl,type,
butlast:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(last_decl,type,
last:
!>[TA: $tType] : ( ( TA @ list ) > TA ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) ) ).
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_all_decl,type,
list_all:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
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(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(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(i_decl,type,
i: nat ).
thf(rs_decl,type,
rs: dB @ list ).
thf(118,axiom,
! [A: dB @ list,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( ( A
!= ( dB @ nil ) )
=> ? [E: dB @ list] :
( ( D
= ( E @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( A
= ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ) ) )
& ( ( A
= ( dB @ nil ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_App__eq__foldl__conv) ).
thf(697,plain,
! [A: dB @ list,B: dB,C: dB,D: dB] :
( ( ( ( ( A
!= ( dB @ nil ) )
=> ? [E: dB @ list] :
( ( D
= ( E @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( A
= ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ) ) )
& ( ( A
= ( dB @ nil ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= B ) ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( ( A
!= ( dB @ nil ) )
=> ? [E: dB @ list] :
( ( D
= ( E @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
& ( A
= ( dB @ nil @ ( C @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( E @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) ) ) ) )
& ( ( A
= ( dB @ nil ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(72,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(463,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(336,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(73,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_not__Cons__self2) ).
thf(465,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(319,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(108,axiom,
! [A: dB @ list,B: dB,C: nat] :
( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Var__eq__apps__conv) ).
thf(645,plain,
! [A: dB @ list,B: dB,C: nat] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) )
=> ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_last__ConsL) ).
thf(518,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(74,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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(468,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(25,axiom,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_IT_OVar) ).
thf(234,plain,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(103,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( dB @ nil @ ( A @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( B @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_app__last) ).
thf(628,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( dB @ nil @ ( A @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( B @ ( dB @ append @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ list @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(29,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_dB_Osimps_I4_J) ).
thf(249,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(77,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_81_maps__simps_I2_J) ).
thf(481,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)],[77]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_butlast_Osimps_I1_J) ).
thf(352,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ butlast ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_foldl__Cons) ).
thf(170,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_self__append__conv2) ).
thf(582,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(3,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_dB_Osimps_I3_J) ).
thf(120,plain,
! [A: dB,B: dB] :
( ( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ maps ) ) ) @ ( B @ ( C @ ( TB @ list @ ( TA @ aa ) ) ) @ ( TB @ append @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_maps__simps_I1_J) ).
thf(655,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ maps ) ) ) @ ( B @ ( C @ ( TB @ list @ ( TA @ aa ) ) ) @ ( TB @ append @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(114,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_append__self__conv) ).
thf(677,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
& ( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_list__nonempty__induct) ).
thf(384,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( TA @ nil @ ( A @ ( TA @ last ) @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ butlast ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_append__butlast__last__id) ).
thf(142,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ( ( TA @ nil @ ( A @ ( TA @ last ) @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ butlast ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(75,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(472,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(18,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_apps__eq__tail__conv) ).
thf(185,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( C = A )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(35,axiom,
( ( rs @ ( i @ var @ ( app @ ( dB @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( it @ ( dB @ ( bool @ ( dB @ combb ) ) ) ) @ ( dB @ listsp ) ) )
& ( rs @ ( it @ ( dB @ listsp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(288,plain,
( ( rs @ ( i @ var @ ( app @ ( dB @ ( dB @ ( dB @ combc ) ) ) @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( it @ ( dB @ ( bool @ ( dB @ combb ) ) ) ) @ ( dB @ listsp ) ) )
& ( rs @ ( it @ ( dB @ listsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list_Oinject) ).
thf(257,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_append__Nil) ).
thf(460,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_last_Osimps) ).
thf(157,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(106,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Cons__eq__appendI) ).
thf(638,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_splice__Nil2) ).
thf(421,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(43,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Nil__is__append__conv) ).
thf(325,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(67,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list_Oexhaust) ).
thf(448,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_not__Cons__self) ).
thf(316,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(164,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(98,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( A @ ( TA @ butlast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_butlast__append) ).
thf(591,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( A @ ( TA @ butlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(42,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_dB_Osimps_I8_J) ).
thf(321,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(30,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_dB_Osimps_I5_J) ).
thf(253,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(83,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Var__apps__neq__Abs__apps) ).
thf(514,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(10,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Abs__eq__apps__conv) ).
thf(147,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) )
=> ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(105,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_last__appendL) ).
thf(634,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(6,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_98_rev__is__rev__conv) ).
thf(133,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)],[6]) ).
thf(36,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_eq__Nil__appendI) ).
thf(292,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(55,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_append__eq__appendI) ).
thf(380,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(661,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(89,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_last__append) ).
thf(546,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( A @ ( TA @ last ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_last__ConsR) ).
thf(201,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: dB] :
( ! [B: nat] :
( A
!= ( B @ var ) )
=> ( ! [B: dB,C: dB] :
( A
!= ( C @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ! [B: dB] :
( A
!= ( B @ abs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_dB_Oexhaust) ).
thf(220,plain,
! [A: dB] :
( ! [B: nat] :
( A
!= ( B @ var ) )
=> ( ! [B: dB,C: dB] :
( A
!= ( C @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ! [B: dB] :
( A
!= ( B @ abs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(334,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(349,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(99,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(598,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)],[99]) ).
thf(57,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( A
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_listsp_Osimps) ).
thf(392,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( 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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( A
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(62,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_append__assoc) ).
thf(424,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(65,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_insert__Nil) ).
thf(435,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(522,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(93,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_list__all__simps_I2_J) ).
thf(566,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(78,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_same__append__eq) ).
thf(484,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_dB_Osimps_I10_J) ).
thf(285,plain,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_dB_Osimps_I1_J) ).
thf(224,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_foldl__fun__comm) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(19,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( TA @ list_all ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_list__all__append) ).
thf(193,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( TA @ list_all ) ) ) )
=> ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( TA @ list_all ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(107,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_append__Nil2) ).
thf(642,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_butlast__snoc) ).
thf(457,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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_25_list_Osimps_I5_J) ).
thf(173,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( 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)],[15]) ).
thf(101,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Cons__eq__append__conv) ).
thf(605,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_append__eq__append__conv2) ).
thf(266,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( E @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(113,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Osimps_I3_J) ).
thf(674,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
<=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_listsp__conj__eq) ).
thf(430,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) )
=> ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) ) )
& ( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( TB @ nil @ ( TB @ rotate1 ) )
= ( TB @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_rotate__simps) ).
thf(296,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rotate1 ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( ( TB @ nil @ ( TB @ rotate1 ) )
= ( TB @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(100,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_dB_Osimps_I6_J) ).
thf(601,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(16,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_neq__Nil__conv) ).
thf(176,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(117,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_dB_Osimps_I11_J) ).
thf(694,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(95,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_list__all__simps_I1_J) ).
thf(577,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(22,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_append__eq__Cons__conv) ).
thf(204,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_splice_Osimps_I3_J) ).
thf(313,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_last__snoc) ).
thf(236,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(58,axiom,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_dB_Osimps_I12_J) ).
thf(406,plain,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(68,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_rev__cases) ).
thf(451,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(38,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_dB_Osimps_I2_J) ).
thf(303,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(494,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(104,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_splice_Osimps_I1_J) ).
thf(631,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(53,axiom,
! [A: dB] :
? [B: dB @ list,C: dB] :
( ( ? [D: dB] :
( C
= ( D @ abs ) )
| ? [D: nat] :
( C
= ( D @ var ) ) )
& ( A
= ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ex__head__tail) ).
thf(367,plain,
! [A: dB] :
? [B: dB @ list,C: dB] :
( ( ? [D: dB] :
( C
= ( D @ abs ) )
| ? [D: nat] :
( C
= ( D @ var ) ) )
& ( A
= ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(7,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Lambda) ).
thf(140,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rotate1__is__Nil__conv) ).
thf(621,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)],[102]) ).
thf(20,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_rev_Osimps_I2_J) ).
thf(198,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(130,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Abs__apps__eq__Abs__apps__conv) ).
thf(438,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(110,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_24_list_Osimps_I4_J) ).
thf(658,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)],[110]) ).
thf(97,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(589,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(47,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_dB_Osimps_I7_J) ).
thf(342,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_append1__eq__conv) ).
thf(355,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(90,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( C
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_rev__eq__Cons__iff) ).
thf(553,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( C
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( C
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(9,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Var__IT) ).
thf(145,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(86,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_append__Cons) ).
thf(525,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(33,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) )
= ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rotate1__def) ).
thf(282,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) )
= ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ append @ ( TA @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_butlast_Osimps_I2_J) ).
thf(414,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( B @ ( TA @ butlast ) @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ butlast ) )
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(59,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listsp ) ) )
<=> ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_append__in__listsp__conv) ).
thf(409,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listsp ) ) ) )
& ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ listsp ) ) )
=> ( ( A @ ( C @ ( TA @ listsp ) ) )
& ( B @ ( C @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(94,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_append__is__Nil__conv) ).
thf(568,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1,conjecture,
dB @ nil @ ( i @ var @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( dB @ nil @ ( i @ var @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( dB @ nil @ ( i @ var @ ( dB @ cons @ ( dB @ list @ ( dB @ list @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ list @ ( dB @ list @ aa ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(115,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_rev__is__Nil__conv) ).
thf(684,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)],[115]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_foldl__Nil) ).
thf(346,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(13,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_listsp_ONil) ).
thf(168,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_list__ex1__simps_I1_J) ).
thf(183,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_self__append__conv) ).
thf(373,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(92,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(564,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(82,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_ex1 ) ) )
<=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_list__ex1__simps_I2_J) ).
thf(506,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) )
=> ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_ex1 ) ) )
=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_append__same__eq) ).
thf(474,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(112,axiom,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Var__apps__eq__Var__apps__conv) ).
thf(664,plain,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(88,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
<=> ( ( ( A @ ( TA @ last ) )
= B )
& ( ( A @ ( TA @ butlast ) )
= C )
& ( A
!= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_snoc__eq__iff__butlast) ).
thf(532,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 @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) )
& ( ( ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
=> ( ( ( A @ ( TA @ last ) )
= B )
& ( ( A @ ( TA @ butlast ) )
= C )
& ( A
!= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(27,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_splice_Osimps_I2_J) ).
thf(239,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
<=> ( B
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_append__self__conv2) ).
thf(242,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) )
& ( ( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
=> ( B
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_foldl__append) ).
thf(427,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Abs__App__neq__Var__apps) ).
thf(528,plain,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(5,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(131,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(691,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(91,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_dB_Osimps_I9_J) ).
thf(560,plain,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(79,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rev__exhaust2) ).
thf(491,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(52,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_last__appendR) ).
thf(364,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ( B @ ( A @ ( TA @ append @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ last ) )
= ( B @ ( TA @ last ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(81,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) )
<=> ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_apps__eq__Abs__conv) ).
thf(496,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) )
=> ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(69,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Osimps_I2_J) ).
thf(454,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(800,plain,
$false,
inference(e,[status(thm)],[697,463,336,465,319,645,518,468,234,628,249,481,352,170,582,120,655,677,384,142,472,185,288,257,460,157,638,421,325,448,316,164,591,321,253,514,147,634,133,292,380,661,546,201,220,334,349,598,392,424,435,522,566,484,285,224,339,193,642,457,173,605,266,674,430,296,601,176,694,577,204,313,236,406,451,303,494,631,367,140,621,198,130,438,658,589,342,355,553,145,525,282,414,409,568,119,684,346,168,183,373,564,506,474,664,532,239,242,427,528,131,691,560,491,364,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL769_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/5.50 % Computer : n019.cluster.edu
% 0.24/5.50 % Model : x86_64 x86_64
% 0.24/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.50 % Memory : 8046.5625MB
% 0.24/5.50 % OS : Linux 6.8.0-71-generic
% 0.24/5.50 % CPULimit : 300
% 0.24/5.50 % WCLimit : 300
% 0.24/5.50 % DateTime : Fri Sep 25 23:31:39 UTC 2026
% 0.24/5.51 % CPUTime :
% 0.24/5.51 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
% 1.44/6.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.58/6.79 % [INFO] Parsing done (483ms).
% 3.06/6.81 % [INFO] Running in sequential loop mode.
% 4.21/7.38 % [INFO] eprover registered as external prover.
% 4.21/7.39 % [INFO] Scanning for conjecture ...
% 4.86/7.65 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 5.62/7.86 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 7.48/8.31 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.48/8.36 % [INFO] Type checking passed.
% 7.48/8.37 % [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 ...
% 39.73/23.90 % External prover 'e' found a proof!
% 39.73/23.91 % [INFO] Killing All external provers ...
% 39.73/23.91 % Time passed: 18218ms (effective reasoning time: 17085ms)
% 39.73/23.91 % 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)>
% 39.73/23.91 % Axioms used in derivation (116): fact_77_rotate1__is__Nil__conv, fact_93_butlast_Osimps_I2_J, fact_75_ext, fact_59_dB_Osimps_I8_J, fact_69_rev__induct, fact_9_list_Osimps_I3_J, fact_13_foldl__Cons, fact_47_foldl__append, fact_65_Var__apps__neq__Abs__apps, fact_99_rev__is__Nil__conv, help_COMBS_1_1_U, fact_3_dB_Osimps_I1_J, fact_83_last__snoc, fact_17_Var__eq__apps__conv, fact_66_Abs__App__neq__Var__apps, fact_32_apps__eq__Abs__conv, fact_44_self__append__conv2, fact_62_dB_Osimps_I7_J, fact_10_listsp_Osimps, help_fconj_3_1_U, fact_1_listsp_ONil, fact_49_Lambda, fact_91_append__butlast__last__id, fact_16_not__Cons__self, fact_48_append__in__listsp__conv, fact_30_app__last, fact_95_butlast__snoc, fact_86_last__ConsL, fact_57_append__Nil2, fact_96_rev__eq__Cons__iff, fact_89_last__appendL, fact_98_rev__is__rev__conv, fact_5_list_Oinject, fact_19_apps__eq__tail__conv, fact_87_last__append, fact_34_dB_Osimps_I10_J, fact_0_Var__IT, fact_70_list__ex1__simps_I2_J, fact_45_self__append__conv, fact_35_list__nonempty__induct, fact_18_Var__apps__eq__Var__apps__conv, fact_15_not__Cons__self2, help_fNot_2_1_U, fact_27_splice_Osimps_I1_J, fact_23_splice_Osimps_I2_J, fact_53_dB_Osimps_I12_J, fact_40_append__Cons, help_fNot_1_1_U, fact_55_Cons__eq__appendI, fact_2_listsp__conj__eq, fact_51_Abs__apps__eq__Abs__apps__conv, fact_43_append__is__Nil__conv, fact_50_append1__eq__conv, fact_21_insert__Nil, fact_12_neq__Nil__conv, fact_26_splice_Osimps_I3_J, fact_46_Nil__is__append__conv, help_COMBB_1_1_U, help_fdisj_1_1_U, fact_78_rotate__simps, fact_36_append__same__eq, fact_74_list__all__simps_I2_J, fact_64_append__eq__Cons__conv, fact_52_append__eq__appendI, fact_80_dB_Oexhaust, fact_68_rev__cases, fact_8_list_Osimps_I2_J, help_fconj_2_1_U, fact_56_eq__Nil__appendI, fact_84_last_Osimps, fact_41_append__self__conv2, fact_28_splice__Nil2, fact_54_append__eq__append__conv2, fact_76_list__all__append, help_fequal_1_1_T, fact_25_list_Osimps_I5_J, fact_72_rev__exhaust2, fact_22_foldl__fun__comm, fact_88_last__appendR, fact_24_list_Osimps_I4_J, help_fdisj_2_1_U, fact_38_append__assoc, fact_14_foldl__Nil, fact_33_list__ex1__simps_I1_J, fact_60_dB_Osimps_I9_J, fact_7_dB_Osimps_I5_J, fact_31_Abs__eq__apps__conv, fact_63_Cons__eq__append__conv, fact_42_append__self__conv, help_COMBC_1_1_U, fact_37_same__append__eq, fact_90_snoc__eq__iff__butlast, fact_79_maps__simps_I1_J, help_fequal_2_1_T, fact_82_ex__head__tail, fact_4_dB_Osimps_I2_J, help_fconj_1_1_U, help_fdisj_3_1_U, fact_39_dB_Osimps_I3_J, fact_11_IT_OVar, fact_58_append__Nil, fact_20_list_Oexhaust, fact_85_last__ConsR, fact_81_maps__simps_I2_J, fact_94_butlast__append, help_pp_1_1_U, fact_61_dB_Osimps_I6_J, fact_6_dB_Osimps_I4_J, fact_67_dB_Osimps_I11_J, help_pp_2_1_U, fact_97_rev_Osimps_I2_J, conj_0, fact_71_rotate1__def, fact_29_App__eq__foldl__conv, fact_92_butlast_Osimps_I1_J, fact_73_list__all__simps_I1_J
% 39.73/23.91 % No. of inferences in proof: 236
% 39.73/23.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18218 ms resp. 17085 ms w/o parsing
% 41.19/24.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.19/24.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------