%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM047_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:57:57 AM UTC 2026
% Result : Theorem 32.69s 19.41s
% Output : Refutation 33.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 124
% Syntax : Number of formulae : 250 ( 155 unt; 0 typ; 0 def)
% Number of atoms : 671 ( 264 equ; 0 cnn)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 3378 ( 80 ~; 26 |; 61 &;3092 @)
% ( 19 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 57 usr; 13 con; 0-6 aty)
% Number of variables : 733 ( 0 ^; 712 !; 21 ?; 733 :)
% 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(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(semiring_div_decl,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(div_mod_decl,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
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(listMem_decl,type,
listMem:
!>[TA: $tType] : ( TA > ( TA @ list ) > $o ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_size_decl,type,
list_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ list ) > nat ) ).
thf(list_all_decl,type,
list_all:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(member1_decl,type,
member1:
!>[TA: $tType] : ( ( TA @ list ) > TA > $o ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
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(tl_decl,type,
tl:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(i_Z_decl,type,
i_Z: atom > ( int @ list ) > $o ).
thf(asubst_decl,type,
asubst: int > ( int @ list ) > atom > atom ).
thf(dvd_decl,type,
dvd: int > int > ( int @ list ) > atom ).
thf(c_PresArith_Oatom_OLe_decl,type,
c_PresArith_Oatom_OLe: int > ( int @ list ) > atom ).
thf(nDvd_decl,type,
nDvd: int > int > ( int @ list ) > atom ).
thf(atom_case_decl,type,
atom_case:
!>[TA: $tType] : ( ( TA @ ( int @ list @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > atom > TA ) ).
thf(atom_rec_decl,type,
atom_rec:
!>[TA: $tType] : ( ( TA @ ( int @ list @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > atom > TA ) ).
thf(atom_size_decl,type,
atom_size: atom > nat ).
thf(decr_Z_decl,type,
decr_Z: atom > atom ).
thf(divisor_decl,type,
divisor: atom > int ).
thf(hd_coeff_decl,type,
hd_coeff: atom > int ).
thf(hd_coeff1_decl,type,
hd_coeff1: int > atom > atom ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: atom ).
thf(e_decl,type,
e: int @ list ).
thf(i_decl,type,
i: int ).
thf(int1_decl,type,
int1: int ).
thf(j_decl,type,
j: int ).
thf(list1_decl,type,
list1: int @ list ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_22_zipwith0_Osimps_I1_J) ).
thf(301,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)],[52]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_list_Orecs_I1_J) ).
thf(138,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)],[6]) ).
thf(95,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_not__Cons__self2) ).
thf(468,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(100,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J) ).
thf(481,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(59,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_divisor_Osimps_I3_J) ).
thf(352,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_sublist__singleton) ).
thf(523,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mod__mod__trivial) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(35,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_atom_Osimps_I4_J) ).
thf(247,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(68,axiom,
nat @ semiring_div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Divides_Osemiring__div) ).
thf(379,plain,
nat @ semiring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(84,axiom,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I2_J) ).
thf(440,plain,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mod__self) ).
thf(202,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(103,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ tl ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_tl_Osimps_I2_J) ).
thf(500,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ tl ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(115,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ hd_coeff )
= ( A @ ( int @ list @ ( int @ combk ) @ ( int @ zero_zero @ ( int @ ( int @ list_case ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_hd__coeff_Osimps_I3_J) ).
thf(538,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ hd_coeff )
= ( A @ ( int @ list @ ( int @ combk ) @ ( int @ zero_zero @ ( int @ ( int @ list_case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(121,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(570,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mod__by__1) ).
thf(372,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ tl ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_tl_Osimps_I1_J) ).
thf(189,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ tl ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(80,axiom,
! [A: int,B: int,C: int @ list,D: int] :
( ( int @ nil @ ( A @ ( B @ nDvd ) ) @ ( C @ ( D @ asubst ) ) )
= ( int @ nil @ ( A @ ( B @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I6_J) ).
thf(421,plain,
! [A: int,B: int,C: int @ list,D: int] :
( ( int @ nil @ ( A @ ( B @ nDvd ) ) @ ( C @ ( D @ asubst ) ) )
= ( int @ nil @ ( A @ ( B @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,axiom,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ dvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_atom_Osimps_I5_J) ).
thf(289,plain,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ dvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__Cons__self) ).
thf(448,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(55,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(321,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(32,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_atom_Osimps_I8_J) ).
thf(238,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(25,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_eq__Nil__null) ).
thf(211,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_iprod__Nil) ).
thf(253,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(73,axiom,
! [A: int @ list,B: int,C: atom] :
( ( ( C @ hd_coeff )
= ( int @ zero_zero ) )
=> ( ( A @ ( B @ ( int @ cons ) ) @ ( C @ i_Z ) )
<=> ( A @ ( C @ decr_Z @ i_Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Z_Onot__dep__decr) ).
thf(397,plain,
! [A: int @ list,B: int,C: atom] :
( ( ( C @ hd_coeff )
= ( int @ zero_zero ) )
=> ( ( ( A @ ( C @ decr_Z @ i_Z ) )
=> ( A @ ( B @ ( int @ cons ) ) @ ( C @ i_Z ) ) )
& ( ( A @ ( B @ ( int @ cons ) ) @ ( C @ i_Z ) )
=> ( A @ ( C @ decr_Z @ i_Z ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(48,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(293,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(132,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_atom_Osimps_I6_J) ).
thf(133,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__reorient) ).
thf(265,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(30,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_atom_Osize_I4_J) ).
thf(233,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(69,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_sublist__nil) ).
thf(380,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_list_Osimps_I5_J) ).
thf(529,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_iprod__Nil2) ).
thf(220,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(113,axiom,
a @ ( fTrue @ ( int @ list @ ( bool @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( bool @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( fTrue @ ( int @ list @ ( bool @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( bool @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( fFalse @ ( int @ list @ ( bool @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( bool @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ aa ) ) ) @ ( bool @ atom_case ) ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(534,plain,
a @ ( fTrue @ ( int @ list @ ( bool @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( bool @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( fTrue @ ( int @ list @ ( bool @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( bool @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( fFalse @ ( int @ list @ ( bool @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( bool @ aa ) ) ) @ ( int @ ( bool @ ( int @ list @ fun ) @ combk ) @ ( bool @ ( int @ list @ fun ) @ ( int @ fun ) @ ( bool @ ( int @ list @ fun ) @ aa ) ) ) @ ( bool @ atom_case ) ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(58,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ divisor )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_divisor_Osimps_I2_J) ).
thf(349,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ divisor )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(118,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_atom_Osimps_I11_J) ).
thf(561,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(81,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list_Oexhaust) ).
thf(424,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(19,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(192,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(137,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(165,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(94,axiom,
int @ semiring_div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(467,plain,
int @ semiring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(101,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_neq__Nil__conv) ).
thf(484,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(62,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_list_Osize_I1_J) ).
thf(361,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list__all__simps_I1_J) ).
thf(435,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(92,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_divisor_Osimps_I1_J) ).
thf(461,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(74,axiom,
! [A: int] :
( ( A @ ( A @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zmod__self) ).
thf(403,plain,
! [A: int] :
( ( A @ ( A @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_splice__Nil2) ).
thf(141,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(108,axiom,
( a
= ( list1 @ ( int1 @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Le) ).
thf(519,plain,
( a
= ( list1 @ ( int1 @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(125,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_null__rec_I1_J) ).
thf(578,plain,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(96,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ hd_coeff )
= ( A @ ( int @ list @ ( int @ combk ) @ ( int @ zero_zero @ ( int @ ( int @ list_case ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_hd__coeff_Osimps_I2_J) ).
thf(471,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ hd_coeff )
= ( A @ ( int @ list @ ( int @ combk ) @ ( int @ zero_zero @ ( int @ ( int @ list_case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(38,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_atom_Osize_I3_J) ).
thf(256,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(173,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(104,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zipwith0_Osimps_I3_J) ).
thf(503,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(34,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ atom_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_atom_Osize_I1_J) ).
thf(244,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ atom_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zero__neq__one) ).
thf(205,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(116,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_splice_Osimps_I3_J) ).
thf(541,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(50,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(298,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(77,axiom,
! [A: int,B: int,C: int] :
( ( int @ nil @ ( A @ ( B @ nDvd ) ) @ ( C @ hd_coeff1 ) )
= ( int @ nil @ ( A @ ( B @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_hd__coeff1_Osimps_I6_J) ).
thf(412,plain,
! [A: int,B: int,C: int] :
( ( int @ nil @ ( A @ ( B @ nDvd ) ) @ ( C @ hd_coeff1 ) )
= ( int @ nil @ ( A @ ( B @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(166,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(44,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_atom_Osize_I6_J) ).
thf(279,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(66,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_list__ex1__simps_I1_J) ).
thf(375,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_List_Onull__def) ).
thf(176,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) )
& ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list_Osimps_I4_J) ).
thf(286,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ nDvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_atom_Osimps_I7_J) ).
thf(259,plain,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ nDvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(86,axiom,
! [A: atom] :
( ( ( A @ hd_coeff )
= ( int @ zero_zero ) )
=> ( ( ( A @ divisor )
!= ( int @ zero_zero ) )
=> ( ( A @ decr_Z @ divisor )
!= ( int @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Z_Oanormal__decr) ).
thf(445,plain,
! [A: atom] :
( ( ( A @ hd_coeff )
= ( int @ zero_zero ) )
=> ( ( ( A @ divisor )
!= ( int @ zero_zero ) )
=> ( ( A @ decr_Z @ divisor )
!= ( int @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(123,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zmod__zero) ).
thf(572,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(8,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_atom_Osimps_I3_J) ).
thf(144,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(236,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(75,axiom,
! [A: int,B: int,C: int] :
( ( int @ nil @ ( A @ ( B @ dvd ) ) @ ( C @ hd_coeff1 ) )
= ( int @ nil @ ( A @ ( B @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_hd__coeff1_Osimps_I5_J) ).
thf(406,plain,
! [A: int,B: int,C: int] :
( ( int @ nil @ ( A @ ( B @ dvd ) ) @ ( C @ hd_coeff1 ) )
= ( int @ nil @ ( A @ ( B @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(67,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_null__rec_I2_J) ).
thf(377,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(54,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_splice_Osimps_I1_J) ).
thf(318,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list__nonempty__induct) ).
thf(509,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(208,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)],[24]) ).
thf(88,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_list_Osimps_I2_J) ).
thf(451,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(120,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_atom_Orecs_I3_J) ).
thf(567,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(98,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(477,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(114,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ decr_Z )
= ( A @ ( int @ tl ) @ ( B @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_decr_092_060_094isub_062Z_Osimps_I1_J) ).
thf(535,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ decr_Z )
= ( A @ ( int @ tl ) @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(56,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_atom_Osimps_I2_J) ).
thf(323,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(36,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(251,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_insert) ).
thf(521,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(90,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ hd_coeff )
= ( A @ ( int @ list @ ( int @ combk ) @ ( int @ zero_zero @ ( int @ ( int @ list_case ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_hd__coeff_Osimps_I1_J) ).
thf(455,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ hd_coeff )
= ( A @ ( int @ list @ ( int @ combk ) @ ( int @ zero_zero @ ( int @ ( int @ list_case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(28,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(223,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(72,axiom,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_atom_Orecs_I1_J) ).
thf(394,plain,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(51,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(299,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(29,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_equal__list__def) ).
thf(226,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ list @ equal_equal ) ) ) )
& ( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
! [A: atom] :
( ! [B: int,C: int @ list] :
( A
!= ( C @ ( B @ c_PresArith_Oatom_OLe ) ) )
=> ( ! [B: int,C: int,D: int @ list] :
( A
!= ( D @ ( C @ ( B @ dvd ) ) ) )
=> ~ ! [B: int,C: int,D: int @ list] :
( A
!= ( D @ ( C @ ( B @ nDvd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_atom_Oexhaust) ).
thf(167,plain,
! [A: atom] :
( ! [B: int,C: int @ list] :
( A
!= ( C @ ( B @ c_PresArith_Oatom_OLe ) ) )
=> ( ! [B: int,C: int,D: int @ list] :
( A
!= ( D @ ( C @ ( B @ dvd ) ) ) )
=> ~ ! [B: int,C: int,D: int @ list] :
( A
!= ( D @ ( C @ ( B @ nDvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_atom_Osize_I5_J) ).
thf(162,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(355,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) @ ( B @ hd_coeff1 ) )
= ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_hd__coeff1_Osimps_I4_J) ).
thf(458,plain,
! [A: int,B: int] :
( ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) @ ( B @ hd_coeff1 ) )
= ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ div_mod ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mod__by__0) ).
thf(295,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ div_mod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(45,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(282,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)],[45]) ).
thf(76,axiom,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_atom_Osimps_I10_J) ).
thf(409,plain,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(40,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_member__rec_I2_J) ).
thf(263,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mod__0) ).
thf(199,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(117,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ listMem ) ) )
<=> ( ? [C: TA,D: TA @ list,E: TA] :
( ( D @ ( C @ ( TA @ listMem ) ) )
& ( A
= ( D @ ( E @ ( TA @ cons ) ) ) )
& ( B = C ) )
| ? [C: TA,D: TA @ list] :
( ( A
= ( D @ ( C @ ( TA @ cons ) ) ) )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_ListMem_Osimps) ).
thf(544,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( ? [C: TA,D: TA @ list,E: TA] :
( ( D @ ( C @ ( TA @ listMem ) ) )
& ( A
= ( D @ ( E @ ( TA @ cons ) ) ) )
& ( B = C ) )
| ? [C: TA,D: TA @ list] :
( ( A
= ( D @ ( C @ ( TA @ cons ) ) ) )
& ( B = C ) ) )
=> ( A @ ( B @ ( TA @ listMem ) ) ) )
& ( ( A @ ( B @ ( TA @ listMem ) ) )
=> ( ? [C: TA,D: TA @ list,E: TA] :
( ( D @ ( C @ ( TA @ listMem ) ) )
& ( A
= ( D @ ( E @ ( TA @ cons ) ) ) )
& ( B = C ) )
| ? [C: TA,D: TA @ list] :
( ( A
= ( D @ ( C @ ( TA @ cons ) ) ) )
& ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) )
<=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list__ex1__simps_I2_J) ).
thf(386,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) )
=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(122,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(571,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(26,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list__all__simps_I2_J) ).
thf(218,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(64,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_equal__Nil__null) ).
thf(368,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) ) )
& ( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(107,axiom,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(517,plain,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(53,axiom,
! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_atom_Osimps_I1_J) ).
thf(304,plain,
! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) )
& ( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(186,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)],[17]) ).
thf(13,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(171,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ decr_Z )
= ( A @ ( int @ tl ) @ ( B @ ( C @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_decr_092_060_094isub_062Z_Osimps_I3_J) ).
thf(418,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ decr_Z )
= ( A @ ( int @ tl ) @ ( B @ ( C @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(99,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_splice_Osimps_I2_J) ).
thf(478,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(70,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_insert__Nil) ).
thf(383,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_one__neq__zero) ).
thf(183,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(42,axiom,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_divisor__asubst) ).
thf(273,plain,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(119,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_atom_Osimps_I12_J) ).
thf(564,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(33,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(242,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
( ( e @ ( i @ ( int @ cons ) ) @ ( a @ i_Z ) )
<=> ( e @ ( j @ ( int @ cons ) ) @ ( a @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( e @ ( i @ ( int @ cons ) ) @ ( a @ i_Z ) )
<=> ( e @ ( j @ ( int @ cons ) ) @ ( a @ i_Z ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(126,plain,
~ ( ( ( e @ ( j @ ( int @ cons ) ) @ ( a @ i_Z ) )
=> ( e @ ( i @ ( int @ cons ) ) @ ( a @ i_Z ) ) )
& ( ( e @ ( i @ ( int @ cons ) ) @ ( a @ i_Z ) )
=> ( e @ ( j @ ( int @ cons ) ) @ ( a @ i_Z ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_zero__reorient) ).
thf(341,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)],[57]) ).
thf(105,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Osimps_I3_J) ).
thf(506,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(61,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_atom_Osize_I2_J) ).
thf(358,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(20,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_atom_Osimps_I9_J) ).
thf(195,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(97,axiom,
! [A: int,B: int @ list,C: int] :
( ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) @ ( B @ ( C @ asubst ) ) )
= ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_asubst_Osimps_I4_J) ).
thf(474,plain,
! [A: int,B: int @ list,C: int] :
( ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) @ ( B @ ( C @ asubst ) ) )
= ( int @ nil @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(112,axiom,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_elem) ).
thf(532,plain,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(78,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_atom_Orecs_I2_J) ).
thf(415,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(93,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 ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zipwith0_Osimps_I2_J) ).
thf(464,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 ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Orecs_I2_J) ).
thf(575,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 ) ) )
<=> ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_member__rec_I1_J) ).
thf(427,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 ) ) )
=> ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(85,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ decr_Z )
= ( A @ ( int @ tl ) @ ( B @ ( C @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_decr_092_060_094isub_062Z_Osimps_I2_J) ).
thf(442,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ decr_Z )
= ( A @ ( int @ tl ) @ ( B @ ( C @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(102,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_list_Oinject) ).
thf(491,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(89,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(454,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(364,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(581,plain,
$false,
inference(e,[status(thm)],[301,138,468,481,352,523,276,247,379,440,202,500,538,570,372,189,421,289,448,321,238,211,253,397,293,132,133,265,233,380,529,220,534,349,561,424,192,137,165,467,484,361,435,461,403,141,519,578,471,256,173,503,244,205,541,298,412,166,279,375,176,286,259,445,572,144,236,406,377,318,509,208,451,567,477,535,323,251,521,455,223,394,299,226,167,162,355,458,295,282,409,263,199,544,386,571,218,368,517,304,186,171,418,478,383,183,273,564,242,126,341,506,358,195,474,532,415,464,575,427,442,491,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM047_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 23:24:47 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.79/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.21 % [INFO] Parsing done (335ms).
% 1.82/1.22 % [INFO] Running in sequential loop mode.
% 2.98/1.61 % [INFO] eprover registered as external prover.
% 2.98/1.62 % [INFO] Scanning for conjecture ...
% 3.26/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 123 axioms. Running axiom selection ...
% 3.84/1.90 % [INFO] Axiom selection finished. Selected 123 axioms (removed 0 axioms).
% 4.32/2.12 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.61/2.15 % [INFO] Type checking passed.
% 4.61/2.16 % [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 ...
% 5.83/2.62 % [INFO] [Domain constraints] Detected constraint on bool
% 5.83/2.62 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 5.83/2.66 % [INFO] [Domain constraints] Detected constraint on bool
% 5.83/2.67 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 32.69/19.41 % External prover 'e' found a proof!
% 32.69/19.41 % [INFO] Killing All external provers ...
% 32.69/19.41 % Time passed: 18918ms (effective reasoning time: 18185ms)
% 32.69/19.41 % 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)>
% 32.69/19.41 % Axioms used in derivation (123): fact_35_insert__Nil, fact_26_list_Osimps_I4_J, fact_43_mod__self, help_COMBS_1_1_U, arity_Int_Oint___Groups_Oone, fact_63_atom_Osize_I2_J, fact_57_hd__coeff_Osimps_I2_J, fact_86_list__nonempty__induct, fact_17_mod__mod__trivial, fact_68_atom_Osimps_I9_J, fact_25_list_Osimps_I3_J, fact_88_tl_Osimps_I1_J, fact_71_atom_Osimps_I5_J, fact_2_list_Oinject, fact_50_atom_Osize_I4_J, fact_13_insert, help_fTrue_1_1_T, arity_Int_Oint___Rings_Oring, fact_23_member__rec_I2_J, fact_45_mod__by__1, fact_14_divisor_Osimps_I1_J, fact_19_ListMem_Osimps, fact_54_list__all__simps_I1_J, fact_69_atom_Osimps_I8_J, fact_85_atom_Orecs_I1_J, fact_61_sublist__nil, help_fNot_2_1_U, help_fTrue_1_1_U, fact_29_splice_Osimps_I1_J, fact_73_mem__def, arity_Nat_Onat___Divides_Osemiring__div, fact_60_atom_Osimps_I3_J, help_fNot_1_1_U, fact_4_assms_I2_J, fact_89_decr_092_060_094isub_062Z_Osimps_I1_J, help_fFalse_1_1_T, fact_18_one__reorient, fact_97_hd__coeff1_Osimps_I5_J, fact_12_elem, fact_27_eq__Nil__null, fact_76_atom_Osimps_I12_J, fact_34_list_Oexhaust, fact_59_atom_Osimps_I2_J, help_COMBB_1_1_U, fact_37_zipwith0_Osimps_I3_J, fact_93_hd__coeff1_Osimps_I6_J, fact_83_atom_Orecs_I3_J, fact_11_zipwith0_Osimps_I2_J, fact_9_list_Orecs_I2_J, fact_6_not__Cons__self2, fact_30_List_Onull__def, fact_46_zero__reorient, help_fdisj_1_1_U, fact_92_asubst_Osimps_I6_J, fact_75_atom_Osimps_I11_J, fact_41_zmod__self, fact_39_list__ex1__simps_I1_J, fact_55_list__all__simps_I2_J, fact_58_sublist__singleton, fact_66_divisor_Osimps_I2_J, fact_72_atom_Osimps_I6_J, fact_5_not__Cons__self, fact_33_neq__Nil__conv, fact_81_iprod__Nil2, fact_28_splice__Nil2, fact_20_member__rec_I1_J, fact_49_atom_Osize_I1_J, help_fequal_1_1_T, fact_94_divisor__asubst, fact_77_Z_Onot__dep__decr, fact_74_atom_Osimps_I7_J, fact_0_Le, fact_52_one__neq__zero, fact_47_equal__list__def, arity_Nat_Onat___Groups_Ozero, fact_40_zmod__zero, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_56_hd__coeff_Osimps_I3_J, fact_82_iprod__Nil, fact_15_atom_Osimps_I1_J, fact_1_assms_I3_J, fact_21_splice_Osimps_I2_J, fact_78_atom_Oexhaust, fact_96_asubst_Osimps_I4_J, fact_8_splice_Osimps_I3_J, fact_79_list_Osize_I1_J, fact_53_list__ex1__simps_I2_J, fact_7_list_Osimps_I5_J, fact_51_zero__neq__one, help_fequal_2_1_T, fact_3_assms_I1_J, fact_65_atom_Osize_I3_J, fact_24_list_Osimps_I2_J, fact_16_atom_Osimps_I10_J, help_fdisj_3_1_U, arity_Int_Oint___Rings_Ozero__neq__one, fact_32_list_Orecs_I1_J, fact_44_hd__coeff_Osimps_I1_J, fact_36_equal__Nil__null, arity_Nat_Onat___Groups_Oone, fact_67_divisor_Osimps_I3_J, fact_31_null__rec_I2_J, help_fFalse_1_1_U, fact_91_tl_Osimps_I2_J, fact_84_atom_Orecs_I2_J, fact_70_atom_Osimps_I4_J, fact_62_atom_Osize_I5_J, help_pp_1_1_U, fact_10_null__rec_I1_J, fact_48_mod__by__0, arity_Int_Oint___Divides_Osemiring__div, fact_90_decr_092_060_094isub_062Z_Osimps_I2_J, fact_42_mod__0, fact_22_zipwith0_Osimps_I1_J, fact_95_hd__coeff1_Osimps_I4_J, arity_Int_Oint___Groups_Ozero, help_pp_2_1_U, fact_87_decr_092_060_094isub_062Z_Osimps_I3_J, fact_38_zipwith0_Osimps_I4_J, arity_Nat_Onat___Rings_Ozero__neq__one, fact_80_Z_Oanormal__decr, fact_64_atom_Osize_I6_J
% 32.69/19.41 % No. of inferences in proof: 250
% 32.69/19.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18918 ms resp. 18185 ms w/o parsing
% 33.15/19.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.15/19.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------