%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM081_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 06:58:00 AM UTC 2026
% Result : Theorem 97.64s 79.21s
% Output : Refutation 98.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 108
% Syntax : Number of formulae : 218 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 2428 ( 313 equ; 0 cnn)
% Maximal formula atoms : 20 ( 11 avg)
% Number of connectives : 7500 ( 55 ~; 2 |; 76 &;7169 @)
% ( 21 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 10 con; 0-6 aty)
% Number of variables : 742 ( 0 ^; 697 !; 45 ?; 742 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
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(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) ).
thf(n_lists_decl,type,
n_lists:
!>[TA: $tType] : ( nat > ( TA @ list ) > ( TA @ list @ list ) ) ).
thf(product_decl,type,
product:
!>[TA: $tType,TB: $tType] : ( ( TB @ list ) > ( TA @ list ) > ( TA @ ( TB @ product_prod ) @ list ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(iprod_decl,type,
iprod:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > TA ) ).
thf(zipwith0_decl,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TC @ list ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(concat_decl,type,
concat:
!>[TA: $tType] : ( ( TA @ list @ list ) > ( TA @ list ) ) ).
thf(dropWhile_decl,type,
dropWhile:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
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 ) ) > ( TB @ ( TA @ list @ fun ) ) ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_size_decl,type,
list_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ list ) > nat ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ fun ) ) ).
thf(maps_decl,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TA @ list @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(remdups_decl,type,
remdups:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( TA @ fun ) ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(sublist_decl,type,
sublist:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( nat @ fun ) ) > ( TA @ list ) ) ).
thf(transpose_decl,type,
transpose:
!>[TA: $tType] : ( ( TA @ list @ list ) > ( TA @ list @ list ) ) ).
thf(transpose_rel_decl,type,
transpose_rel:
!>[TA: $tType] : ( bool @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ fun ) ) ).
thf(interpret_decl,type,
interpret:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TA @ list @ fun ) @ ( TB @ fun ) ) > ( TB @ fm ) > ( TA @ list ) > $o ) ).
thf(list_conj_decl,type,
list_conj:
!>[TA: $tType] : ( ( TA @ fm @ list ) > ( TA @ fm ) ) ).
thf(list_disj_decl,type,
list_disj:
!>[TA: $tType] : ( ( TA @ fm @ list ) > ( TA @ fm ) ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(i_Z_decl,type,
i_Z: bool @ ( int @ list @ fun ) @ ( atom @ fun ) ).
thf(asubst_decl,type,
asubst: int > ( int @ list ) > atom > atom ).
thf(divisor_decl,type,
divisor: atom > int ).
thf(lbounds_decl,type,
lbounds: ( atom @ list ) > ( int @ list @ ( int @ product_prod ) @ list ) ).
thf(qEpres896714165pres_1_decl,type,
qEpres896714165pres_1: ( atom @ list ) > ( atom @ fm ) ).
thf(accp_decl,type,
accp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) > TA > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(as_decl,type,
as: atom @ list ).
thf(xs_decl,type,
xs: int @ list ).
thf(16,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Suc__neq__Zero) ).
thf(170,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Zero__neq__Suc) ).
thf(153,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ remdups ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_remdups_Osimps_I1_J) ).
thf(135,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ remdups ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(190,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(59,axiom,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_norm) ).
thf(347,plain,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list] :
( ! [D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( C @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_map__ext) ).
thf(468,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list] :
( ! [D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( C @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_map__eq__Cons__D) ).
thf(481,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ list] :
( ? [C: TA @ list] :
( B
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ! [C: TB] :
( ( B @ ( TB @ set ) @ ( C @ ( TB @ member ) ) )
=> ? [D: TA] :
( C
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ex__map__conv) ).
thf(365,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ list] :
( ( ! [C: TB] :
( ( B @ ( TB @ set ) @ ( C @ ( TB @ member ) ) )
=> ? [D: TA] :
( C
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ? [C: TA @ list] :
( B
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ? [C: TA @ list] :
( B
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ! [C: TB] :
( ( B @ ( TB @ set ) @ ( C @ ( TB @ member ) ) )
=> ? [D: TA] :
( C
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_iprod__Nil2) ).
thf(138,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_list_Orecs_I1_J) ).
thf(174,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(49,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_transpose_Osimps_I2_J) ).
thf(301,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(77,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ),B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ( TA @ aa ) ) ) )
= C ) )
=> ( ( B @ ( A @ ( TA @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_map__idI) ).
thf(436,plain,
! [TA: $tType,A: TA @ ( TA @ fun ),B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ( TA @ aa ) ) ) )
= C ) )
=> ( ( B @ ( A @ ( TA @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(56,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_in__set__insert) ).
thf(320,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( TC @ nil @ ( B @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( TC @ zero_zero @ ( B @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zipwith0__Nil) ).
thf(565,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( TC @ nil @ ( B @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( TC @ zero_zero @ ( B @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_transpose_Opsimps_I1_J) ).
thf(389,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1,conjecture,
? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(110,plain,
~ ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_remdups__remdups) ).
thf(157,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(104,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( C @ ( TA @ dropWhile ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dropWhile_Osimps_I2_J) ).
thf(559,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ dropWhile ) ) )
= ( A @ ( C @ ( TA @ dropWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J) ).
thf(284,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(32,axiom,
! [TA: $tType,A: TA @ list,B: nat] :
( ( A @ ( B @ suc @ ( TA @ n_lists ) ) )
= ( A @ ( B @ ( TA @ n_lists ) ) @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ fun ) @ combb ) ) ) ) @ ( TA @ list @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_n__lists_Osimps_I2_J) ).
thf(228,plain,
! [TA: $tType,A: TA @ list,B: nat] :
( ( A @ ( B @ suc @ ( TA @ n_lists ) ) )
= ( A @ ( B @ ( TA @ n_lists ) ) @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ ( TA @ fun ) @ combb ) ) ) ) @ ( TA @ list @ list @ ( TA @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_concat__map__maps) ).
thf(448,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(54,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(316,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ remdups ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ remdups ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ remdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_remdups__map__remdups) ).
thf(453,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ remdups ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ remdups ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ remdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(26,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_dropWhile_Osimps_I1_J) ).
thf(206,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_not__in__set__insert) ).
thf(307,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ transpose ) )
= ( A @ ( TA @ transpose ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_transpose__map__map) ).
thf(248,plain,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ transpose ) )
= ( A @ ( TA @ transpose ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_map_Osimps_I1_J) ).
thf(534,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(40,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ set ) )
= ( A @ ( TA @ set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_set__remdups) ).
thf(260,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ set ) )
= ( A @ ( TA @ set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ remdups ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) @ ( TA @ remdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_insert__remdups) ).
thf(160,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ remdups ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) @ ( TA @ remdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Cons__eq__map__D) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(74,axiom,
int @ ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(429,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_iprod__Nil) ).
thf(197,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(108,axiom,
( ( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) )
=> ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096lbounds_Aas_A_126_061_A_091_093_A_061_061_062_AEX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
thf(583,plain,
( ( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) )
=> ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(92,axiom,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_in__set__sublistD) ).
thf(493,plain,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_transpose_Osimps_I1_J) ).
thf(456,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_6_not__Cons__self) ).
thf(317,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)],[55]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_maps__def) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ list @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ maps ) ) ) )
= ( A @ ( B @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_zero__reorient) ).
thf(141,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Nil__is__map__conv) ).
thf(537,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(98,axiom,
! [A: int @ list,B: atom @ fm @ list] :
( ( A @ ( B @ ( atom @ list_conj ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
<=> ! [C: atom @ fm] :
( ( B @ ( atom @ fm @ set ) @ ( C @ ( atom @ fm @ member ) ) )
=> ( A @ ( C @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Z_OI__list__conj) ).
thf(526,plain,
! [A: int @ list,B: atom @ fm @ list] :
( ( ! [C: atom @ fm] :
( ( B @ ( atom @ fm @ set ) @ ( C @ ( atom @ fm @ member ) ) )
=> ( A @ ( C @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) )
=> ( A @ ( B @ ( atom @ list_conj ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) )
& ( ( A @ ( B @ ( atom @ list_conj ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
=> ! [C: atom @ fm] :
( ( B @ ( atom @ fm @ set ) @ ( C @ ( atom @ fm @ member ) ) )
=> ( A @ ( C @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(90,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(489,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',fact_3_list_Oinject) ).
thf(547,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)],[102]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ maps ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_maps__simps_I2_J) ).
thf(212,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)],[28]) ).
thf(6,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_n__not__Suc__n) ).
thf(124,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TC @ cons @ ( TC @ list @ ( TC @ list @ fun ) @ ( TC @ aa ) ) ) @ ( TC @ list @ ( TC @ list @ aa ) ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_zipwith0_Osimps_I2_J) ).
thf(225,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TC @ cons @ ( TC @ list @ ( TC @ list @ fun ) @ ( TC @ aa ) ) ) @ ( TC @ list @ ( TC @ list @ aa ) ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_map__eq__Cons__conv) ).
thf(515,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) @ ( TA @ list @ ( TB @ list @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TB @ list @ aa ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(94,axiom,
( ( ( as @ lbounds )
= ( int @ list @ ( int @ product_prod ) @ nil ) )
=> ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096lbounds_Aas_A_061_A_091_093_A_061_061_062_AEX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
thf(503,plain,
( ( ( as @ lbounds )
= ( int @ list @ ( int @ product_prod ) @ nil ) )
=> ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons @ ( int @ list @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ remdups ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_remdups__eq__nil__iff) ).
thf(128,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ remdups ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ remdups ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_sublist__singleton) ).
thf(586,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ sublist ) ) )
= ( 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)],[109]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_list_Orecs_I2_J) ).
thf(298,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_map_Osimps_I2_J) ).
thf(430,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(79,axiom,
xs @ ( as @ qEpres896714165pres_1 @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096) ).
thf(444,plain,
xs @ ( as @ qEpres896714165pres_1 @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(11,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Suc__n__not__n) ).
thf(149,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_set__ConsD) ).
thf(375,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_splice__Nil2) ).
thf(191,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_11_list_Osimps_I2_J) ).
thf(281,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)],[44]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ concat ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_map__concat) ).
thf(445,plain,
! [TA: $tType,TB: $tType,A: TA @ list @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ concat ) @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ map ) @ ( TB @ list @ list @ ( TA @ list @ list @ fun ) @ ( TB @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TB @ concat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(313,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)],[53]) ).
thf(60,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(350,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(19,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sublist__nil) ).
thf(187,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_23_list_Oexhaust) ).
thf(406,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)],[71]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_24_neq__Nil__conv) ).
thf(274,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)],[43]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_12_list_Osimps_I3_J) ).
thf(245,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)],[36]) ).
thf(96,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_remdups_Osimps_I2_J) ).
thf(509,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_list_Osimps_I5_J) ).
thf(271,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 ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(62,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_transpose_Opsimps_I2_J) ).
thf(362,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ~ ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ~ ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_notin__set__sublistI) ).
thf(451,plain,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ~ ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ~ ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(57,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ list_ex1 ) ) )
<=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_list__ex1__iff) ).
thf(323,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) )
=> ( A @ ( B @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ list_ex1 ) ) )
=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',fact_27_splice_Osimps_I3_J) ).
thf(251,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)],[38]) ).
thf(91,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_map__ident) ).
thf(490,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(426,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)],[73]) ).
thf(27,axiom,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_divisor__asubst) ).
thf(209,plain,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TB @ list] :
( ( A @ ( TA @ nil @ ( TB @ ( TA @ product ) ) ) )
= ( TB @ ( TA @ product_prod ) @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_product_Osimps_I1_J) ).
thf(194,plain,
! [TA: $tType,TB: $tType,A: TB @ list] :
( ( A @ ( TA @ nil @ ( TB @ ( TA @ product ) ) ) )
= ( TB @ ( TA @ product_prod ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ concat ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_concat_Osimps_I1_J) ).
thf(295,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ concat ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(72,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( D @ ( TA @ set ) @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( ( D @ ( B @ ( TA @ dropWhile ) ) )
= ( C @ ( A @ ( TA @ dropWhile ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_dropWhile__cong) ).
thf(409,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( D @ ( TA @ set ) @ ( E @ ( TA @ member ) ) )
=> ( ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( ( D @ ( B @ ( TA @ dropWhile ) ) )
= ( C @ ( A @ ( TA @ dropWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TA @ list,C: TB @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ! [D: TA] :
( ( B @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_map__eq__conv) ).
thf(263,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TA @ list,C: TB @ ( TA @ fun )] :
( ( ! [D: TA] :
( ( B @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( B @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ! [D: TA] :
( ( B @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(310,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_nat_Oinject) ).
thf(177,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(107,axiom,
! [TA: $tType,A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_n__lists__Nil) ).
thf(576,plain,
! [TA: $tType,A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(544,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)],[101]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Cons__eq__map__conv) ).
thf(336,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
=> ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(66,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( nat @ zero_zero @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_n__lists_Osimps_I1_J) ).
thf(386,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( nat @ zero_zero @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TC @ list,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TC @ cons @ ( TC @ list @ ( TC @ list @ fun ) @ ( TC @ aa ) ) ) @ ( TC @ list @ ( TC @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zipwith0_Osimps_I3_J) ).
thf(556,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TC @ list,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TC @ cons @ ( TC @ list @ ( TC @ list @ fun ) @ ( TC @ aa ) ) ) @ ( TC @ list @ ( TC @ list @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ list @ ( TB @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(25,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_list_Osize_I1_J) ).
thf(203,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(93,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( ( A @ ( TA @ concat ) )
= ( TA @ nil ) )
<=> ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_concat__eq__Nil__conv) ).
thf(495,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( TA @ concat ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ concat ) )
= ( TA @ nil ) )
=> ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_18_insert__Nil) ).
thf(465,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)],[86]) ).
thf(33,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ concat ) ) )
<=> ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Nil__eq__concat__conv) ).
thf(231,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) )
=> ( ( TA @ nil )
= ( A @ ( TA @ concat ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( TA @ concat ) ) )
=> ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(50,axiom,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_transpose_Osimps_I3_J) ).
thf(304,plain,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Suc__inject) ).
thf(114,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( ( A @ ( TA @ transpose ) )
= ( TA @ list @ nil ) )
<=> ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_transpose__empty) ).
thf(568,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ) )
& ( ( ( A @ ( TA @ transpose ) )
= ( TA @ list @ nil ) )
=> ! [B: TA @ list] :
( ( A @ ( TA @ list @ set ) @ ( B @ ( TA @ list @ member ) ) )
=> ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TB @ cons @ ( TA @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ list @ ( TB @ list @ ( TA @ combc ) ) ) @ ( TB @ list @ ( TA @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_concat__map__singleton) ).
thf(433,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( A @ ( TB @ nil @ ( B @ ( TB @ cons @ ( TA @ ( TB @ list @ ( TB @ list @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ list @ ( TB @ list @ ( TA @ combc ) ) ) @ ( TB @ list @ ( TA @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ map ) @ ( TB @ list @ list @ ( TA @ list @ fun ) @ ( TB @ list @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ list @ ( TA @ list @ aa ) ) ) @ ( TB @ concat ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(46,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) )
<=> ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dropWhile__eq__Nil__conv) ).
thf(287,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( A @ ( B @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) )
=> ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_splice_Osimps_I1_J) ).
thf(119,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_28_list__nonempty__induct) ).
thf(378,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)],[65]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_7_not__Cons__self2) ).
thf(506,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)],[95]) ).
thf(88,axiom,
! [A: int @ list,B: atom @ fm @ list] :
( ( A @ ( B @ ( atom @ list_disj ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
<=> ? [C: atom @ fm] :
( ( A @ ( C @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
& ( B @ ( atom @ fm @ set ) @ ( C @ ( atom @ fm @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Z_OI__list__disj) ).
thf(474,plain,
! [A: int @ list,B: atom @ fm @ list] :
( ( ? [C: atom @ fm] :
( ( A @ ( C @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
& ( B @ ( atom @ fm @ set ) @ ( C @ ( atom @ fm @ member ) ) ) )
=> ( A @ ( B @ ( atom @ list_disj ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) )
& ( ( A @ ( B @ ( atom @ list_disj ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
=> ? [C: atom @ fm] :
( ( A @ ( C @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
& ( B @ ( atom @ fm @ set ) @ ( C @ ( atom @ fm @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) @ ( TA @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(400,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) @ ( TA @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) @ ( TA @ ( TB @ list @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list_Osimps_I4_J) ).
thf(239,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) @ ( TA @ ( TB @ list @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(35,axiom,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_transpose_Opsimps_I3_J) ).
thf(242,plain,
! [TA: $tType,A: TA @ list @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose_rel @ ( TA @ list @ list @ accp ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ list @ nil @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ ( TA @ list @ combc ) ) ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ list @ ( TA @ list @ fun ) @ combk ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ nil @ ( TA @ ( TA @ list @ list @ list_case ) ) ) @ ( TA @ list @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ list @ concat ) @ ( B @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ transpose ) @ ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ list @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ combk ) @ ( TA @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ combb ) ) ) ) @ ( TA @ nil @ ( TA @ ( TA @ list @ list_case ) ) ) @ ( TA @ list @ ( TA @ list @ map ) @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ ( TA @ list @ fun ) @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) @ ( TA @ concat ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ cons @ ( TA @ list @ list @ ( TA @ list @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ list @ ( TA @ list @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(85,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_List_Oinsert__def) ).
thf(459,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(78,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(442,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ remdups ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_remdups__eq__nil__right__iff) ).
thf(163,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TA @ nil )
= ( A @ ( TA @ remdups ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( TA @ remdups ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TB @ zero ) )
=> ! [A: TA @ ( TC @ fun ) @ ( TB @ fun )] :
( ( TC @ nil @ ( TB @ nil @ ( A @ ( TA @ ( TC @ ( TB @ zipwith0 ) ) ) ) ) )
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zipwith0_Osimps_I1_J) ).
thf(200,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TB @ zero ) )
=> ! [A: TA @ ( TC @ fun ) @ ( TB @ fun )] :
( ( TC @ nil @ ( TB @ nil @ ( A @ ( TA @ ( TC @ ( TB @ zipwith0 ) ) ) ) ) )
= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( C
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_iprod0__if__coeffs0) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( C
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_list__ex1__simps_I1_J) ).
thf(122,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( TA @ set ) @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_map__cong) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( TA @ set ) @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TB @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_map__is__Nil__conv) ).
thf(215,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TB @ nil ) ) )
& ( ( ( A @ ( B @ ( TB @ ( TA @ map ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TB @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_25_splice_Osimps_I2_J) ).
thf(222,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)],[30]) ).
thf(592,plain,
$false,
inference(e,[status(thm)],[170,153,135,190,347,468,481,365,138,174,301,436,320,565,389,110,157,559,284,228,448,316,453,206,307,248,534,260,160,392,429,197,583,493,456,317,403,141,537,526,489,547,212,124,225,515,503,128,586,298,430,444,149,375,191,281,445,313,350,187,406,274,245,509,271,362,451,323,251,490,426,209,194,295,409,263,310,177,576,544,336,386,556,203,495,465,231,304,114,568,433,287,119,378,506,474,400,239,242,459,442,163,200,254,122,354,215,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM081_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/5.60 % Computer : n026.cluster.edu
% 0.15/5.60 % Model : x86_64 x86_64
% 0.15/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.60 % Memory : 8046.5625MB
% 0.15/5.60 % OS : Linux 6.8.0-71-generic
% 0.15/5.60 % CPULimit : 300
% 0.15/5.60 % WCLimit : 300
% 0.15/5.60 % DateTime : Sat Sep 26 23:30:33 UTC 2026
% 0.15/5.61 % CPUTime :
% 0.15/5.61 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.93/6.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/6.53 % [INFO] Parsing done (332ms).
% 1.92/6.54 % [INFO] Running in sequential loop mode.
% 3.04/6.94 % [INFO] eprover registered as external prover.
% 3.04/6.95 % [INFO] Scanning for conjecture ...
% 3.55/7.15 % [INFO] Found a conjecture (or negated_conjecture) and 107 axioms. Running axiom selection ...
% 3.68/7.28 % [INFO] Axiom selection finished. Selected 107 axioms (removed 0 axioms).
% 5.10/7.53 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.10/7.57 % [INFO] Type checking passed.
% 5.10/7.58 % [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 ...
% 97.64/79.20 % External prover 'e' found a proof!
% 97.64/79.20 % [INFO] Killing All external provers ...
% 97.64/79.20 % Time passed: 73450ms (effective reasoning time: 72655ms)
% 97.64/79.20 % 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)>
% 97.64/79.21 % Axioms used in derivation (107): fact_88_transpose_Opsimps_I3_J, fact_89_n__lists_Osimps_I2_J, fact_19_remdups__remdups, fact_95_Suc__inject, fact_3_list_Oinject, fact_87_concat__map__singleton, fact_65_transpose__empty, fact_73_Cons__eq__map__D, fact_30_Z_OI__list__conj, fact_25_splice_Osimps_I2_J, fact_59_map__is__Nil__conv, fact_26_list__ex1__simps_I1_J, fact_43_zipwith0_Osimps_I1_J, fact_12_list_Osimps_I3_J, fact_36_sublist__singleton, fact_35_Z_OI__list__disj, fact_94_Suc__n__not__n, fact_0__096lbounds_Aas_A_126_061_A_091_093_A_061_061_062_AEX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096, fact_70_map__idI, fact_29_product_Osimps_I1_J, fact_79_Nil__eq__concat__conv, help_COMBI_1_1_U, fact_5_norm, fact_34_zero__reorient, fact_8_List_Oinsert__def, fact_44_in__set__sublistD, fact_48_list_Osize_I1_J, fact_18_insert__Nil, fact_56_map__eq__conv, fact_76_map__eq__Cons__D, fact_67_ex__map__conv, fact_75_mem__def, arity_Int_Oint___Rings_Oring, fact_42_zipwith0_Osimps_I2_J, fact_14_set__remdups, fact_55_map_Osimps_I2_J, fact_41_sublist__nil, fact_7_not__Cons__self2, fact_40_list_Orecs_I2_J, fact_4_set__ConsD, fact_16_remdups__eq__nil__right__iff, fact_64_remdups__map__remdups, fact_58_map_Osimps_I1_J, fact_61_dropWhile_Osimps_I1_J, fact_68_map__ext, fact_74_ext, fact_17_remdups__eq__nil__iff, fact_10_remdups_Osimps_I2_J, help_COMBB_1_1_U, fact_37_zipwith0_Osimps_I3_J, fact_6_not__Cons__self, fact_52_transpose_Osimps_I2_J, fact_1__096lbounds_Aas_A_061_A_091_093_A_061_061_062_AEX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096, fact_78_concat_Osimps_I1_J, fact_53_dropWhile__eq__Nil__conv, fact_92_nat_Oinject, fact_91_transpose_Opsimps_I2_J, fact_21_list_Osimps_I4_J, fact_45_notin__set__sublistI, fact_80_map__concat, fact_20_insert__remdups, fact_60_dropWhile_Osimps_I2_J, fact_97_Zero__neq__Suc, fact_23_list_Oexhaust, fact_50_iprod__Nil2, fact_71_Cons__eq__map__conv, arity_Nat_Onat___Groups_Ozero, fact_32_splice__Nil2, fact_31_list__ex1__iff, fact_96_Suc__neq__Zero, fact_72_map__eq__Cons__conv, fact_24_neq__Nil__conv, fact_13_list_Osimps_I5_J, fact_84_transpose_Osimps_I3_J, fact_22_in__set__insert, fact_57_Nil__is__map__conv, fact_83_maps__simps_I2_J, help_COMBK_1_1_U, fact_93_n__not__Suc__n, fact_86_map__ident, help_COMBC_1_1_U, fact_51_iprod0__if__coeffs0, fact_9_not__in__set__insert, fact_39_list_Orecs_I1_J, fact_77_concat__eq__Nil__conv, fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096, fact_15_remdups_Osimps_I1_J, fact_33_splice_Osimps_I1_J, fact_85_divisor__asubst, fact_62_transpose_Osimps_I1_J, fact_28_list__nonempty__induct, fact_81_maps__def, fact_54_zipwith0__Nil, help_pp_1_1_U, fact_90_transpose_Opsimps_I1_J, fact_69_map__cong, arity_Int_Oint___Groups_Ozero, fact_63_transpose__map__map, help_pp_2_1_U, fact_49_iprod__Nil, fact_27_splice_Osimps_I3_J, fact_38_zipwith0_Osimps_I4_J, fact_82_concat__map__maps, fact_11_list_Osimps_I2_J, fact_66_dropWhile__cong, fact_47_n__lists_Osimps_I1_J, fact_46_n__lists__Nil
% 97.64/79.21 % No. of inferences in proof: 218
% 97.64/79.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 73450 ms resp. 72655 ms w/o parsing
% 98.11/79.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 98.11/79.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------